<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>2.0.0.10</Version>
  <hasSegments>false</hasSegments>
  <ReportName>Long-term incentive compensation plan</ReportName>
  <ReportLongName>0219 - Disclosure - Long-term incentive compensation plan</ReportLongName>
  <DisplayLabelColumn>true</DisplayLabelColumn>
  <ShowElementNames>false</ShowElementNames>
  <RoundingOption />
  <HasEmbeddedReports>false</HasEmbeddedReports>
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="12 Months Ended" />
        <Label Id="2" Label="Dec. 31, 2009" />
      </Labels>
      <CurrencyCode>usd</CurrencyCode>
      <CurrencySymbol>$</CurrencySymbol>
      <FootnoteIndexer />
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>USD</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>USDEPS</UnitID>
          <UnitType>Divide</UnitType>
          <NumeratorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </NumeratorMeasure>
          <DenominatorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </DenominatorMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>Long-term incentive compensation plan [Abstract]</Label>
      <Level>0</Level>
      <ElementName>us-gaap_ShareBasedCompensationAbstract</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ElementDataType>string</ElementDataType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>true</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole />
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText />
          <NonNumericTextHeader />
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDefenition>No definition available.</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>Long-term incentive compensation plan</Label>
      <Level>1</Level>
      <ElementName>us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ElementDataType>string</ElementDataType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole>verboselabel</PreferredLabelRole>
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note 19 - us-gaap:DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock--&gt;
   &lt;div style="margin-left: 0%"&gt;
   &lt;div style="margin-top: 12pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;table width="100%" border="0" cellpadding="0" cellspacing="0" style="font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff; text-align: left"&gt;
   &lt;tr&gt;
       &lt;td width="3%"&gt;&lt;/td&gt;
       &lt;td width="97%"&gt;&lt;/td&gt;
   &lt;/tr&gt;
   &lt;tr valign="top"&gt;
       &lt;td&gt;
       &lt;b&gt;&lt;font style="font-family: Arial, Helvetica"&gt;19&amp;#160;&lt;/font&gt;&lt;/b&gt;
   &lt;/td&gt;
       &lt;td&gt;
       &lt;b&gt;&lt;font style="font-family: Arial, Helvetica"&gt;Long-term
       incentive compensation plan&lt;/font&gt;&lt;/b&gt;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;/table&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 3%; margin-right: 0%; text-indent: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
       Since 2008, a long-term incentive compensation plan, was
       implemented.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 3%; margin-right: 0%; text-indent: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
       Under the terms of the plan, the participants, restricted to
       certain executives, may elect to allocate part of their annual
       bonus to the plan. The allocation is applied to purchase
       preferred shares of Vale, through a predefined financial
       institution, at market conditions and with no benefit provided
       by Vale.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 3%; margin-right: 0%; text-indent: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
       The shares purchased by each executive are unrestricted and may,
       at the participant&amp;#8217;s discretion, be sold at any time.
       However, the shares must be held for a three-year period and the
       executive must be continually employed by Vale during that
       period. The participant then becomes entitled to receive from
       Vale a cash payment equivalent to the total amount of shares
       held, based on their market rates. The total shares linked to
       the plan at December&amp;#160;31, 2009 and 2008, were 1,809,117 and
       711,005, respectively.
   &lt;/div&gt;
   &lt;!-- XBRL Pagebreak Begin --&gt;
   &lt;div style="margin-top: 0pt; font-size: 1pt"&gt;
   &lt;/div&gt;
   &lt;div align="center" style="margin-left: 0%; margin-right: 0%; text-indent: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
   &lt;/div&gt;
   &lt;/div&gt;
   &lt;!-- END PAGE WIDTH --&gt;
   &lt;!-- PAGEBREAK --&gt;
   &lt;div style="margin-left: 0%"&gt;
   &lt;!-- BEGIN PAGE WIDTH --&gt;
   &lt;div align="right" style="margin-left: 0%; margin-right: 0%; text-indent: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
   &lt;/div&gt;
   &lt;!-- XBRL Pagebreak End --&gt;
   &lt;div style="margin-top: 3pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 3%; margin-right: 0%; text-indent: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
       Additionally, as a long-term incentive certain eligible
       executives have the opportunity to receive at the end of the
       three-year cycle a certain number of shares at market rates,
       based on an evaluation of their career and performance factors
       measured as an indicator of total return to stockholders.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 3%; margin-right: 0%; text-indent: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
       We account for the compensation cost provided to our executives
       under this long-term incentive compensation plan, following the
       requirements Accounting for Stock-Based Compensation.
       Liabilities are measured at each reporting date at fair value,
       based on market rates. Compensation costs incurred are
       recognized, over the defined three-year vesting period. At
       December&amp;#160;31, 2009 and 2008, we recognized a liability of
       US$72 and US$7, respectively, through the Statement of Income.
   &lt;/div&gt;
   &lt;/div&gt;
</NonNumbericText>
          <NonNumericTextHeader>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDefenition>Disclosure of compensation-related costs for share-based compensation which may include disclosure of policies, compensation plan details, allocation of stock compensation, incentive distributions, share-based arrangements to obtain goods and services, deferred compensation arrangements, employee stock ownership plan details and employee stock purchase plan details.</ElementDefenition>
      <ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 123R
 -Paragraph 64, 65, A240

Reference 2: http://www.xbrl.org/2003/role/presentationRef
 -Publisher AICPA
 -Name Statement of Position (SOP)
 -Number 93-6
 -Paragraph 53

Reference 3: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Staff Accounting Bulletin (SAB)
 -Number Topic 14

</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <ComparabilityReport>false</ComparabilityReport>
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>2</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
