SCHEDULE 13G  
  
Amendment No. 3  
Unifi Incorporated  
Common Stock  
Cusip # 904677101  
Filing Fee: No  
 
 
Cusip # 904677101  
Item 1:	Reporting Person - FMR Corp. - (Tax ID:  04-2507163)  
Item 4:	Commonwealth of Massachusetts  
Item 5:	399,600  
Item 6:	None  
Item 7:	6,735,281  
Item 8:	None  
Item 9:	6,735,281  
Item 11:	9.74%  
Item 12:	HC   
  
  
 
 
Cusip # 904677101  
Item 1:	Reporting Person - Edward C. Johnson 3d - (Tax ID:  ###-##-####)  
Item 4:	United States of America  
Item 5:	None  
Item 6:	None  
Item 7:	6,735,281  
Item 8:	None  
Item 9:	6,735,281  
Item 11:	9.74%  
Item 12:	IN   
  
  
 
 
SCHEDULE 13G - TO BE INCLUDED IN STATEMENTS  
FILED PURSUANT TO RULE 13d-1(b) or 13d-2(b)  
  
  
Item 1(a).	Name of Issuer:  
  
		Unifi Incorporated  
  
Item 1(b).	Name of Issuer's Principal Executive Offices:  
  
		7201 West Friendly Road, P.O. Box 19109  
		Greensboro, NC  27419  
  
Item 2(a).	Name of Person Filing:   
  
		FMR Corp.  
  
Item 2(b).	Address or Principal Business Office or, if None, Residence:  
  
		82 Devonshire Street, Boston, Massachusetts  02109  
  
Item 2(c).	Citizenship:  
  
		Not applicable  
  
Item 2(d).	Title of Class of Securities:  
  
		Common Stock  
  
Item 2(e).	CUSIP Number:    
  
		904677101  
  
Item 3.	This statement is filed pursuant to Rule 13d-1(b) or 13d-2(b) and 
the  
person filing, FMR Corp., is a parent holding company in accordance  
with Section 240.13d-1(b)(ii)(G).  (Note:  See Item 7).  
  
Item 4.	Ownership  
  
	(a)	Amount Beneficially Owned: 
	6,735,281  
  
	(b)	Percent of Class: 
	9.74%  
  
	(c)	Number of shares as to which such person has:    
  
	(i)	sole power to vote or to direct the vote: 
	399,600  
  
	(ii)	shared power to vote or to direct the vote: 
	None  
  
	(iii)	sole power to dispose or to direct the disposition of: 
	6,735,281  
  
	(iv)	shared power to dispose or to direct the disposition of: 
	None  
  
  
 
 
Item 5.	Ownership of Five Percent or Less of a Class.  
  
	Not applicable.  
  
Item 6.	Ownership of More than Five Percent on Behalf of Another Person.  
  
	Various persons have the right to receive or the power to  
direct the receipt of dividends from, or the proceeds from the  
sale of, the common stock of Unifi Incorporated.  No one  
person's interest in the common stock of Unifi Incorporated is  
more than five percent of the total outstanding common stock.  
  
Item 7.	Identification and Classification of the Subsidiary Which Acquired  
the Security Being Reported on By the Parent Holding Company.  
  
	See attached Exhibit(s) A and B.  
  
Item 8.	Identification and Classification of Members of the Group.  
  
	Not applicable, see attached Exhibit A.   
  
Item 9.	Notice of Dissolution of Group.  
  
	Not applicable.  
 
 
Item 10.	Certification.  
  
	By signing below I certify that, to the best of my knowledge  
and belief, the securities referred to above were acquired in  
the ordinary course of business and were not acquired for the  
purpose of and do not have the effect of changing or  
influencing the control of the issuer of such securities and  
were not acquired in connection with or as a participant in any  
transaction having such purpose or effect.  
  
  
Signature  
  
	After reasonable inquiry and to the best of my knowledge and  
belief, I certify that the information set forth in this  
Schedule 13G in connection with FMR Corp's beneficial ownership  
of the common stock of Unifi Incorporated at May 31, 1995 is  
true, complete and correct.   
  
  
  
	June 9, 1995	  
Date  
  
  
  
	/s/Arthur S. Loring  
Signature  
  
  
  
	Arthur S. Loring, Vice  
President	  
Name/Title  
  
  
 
 
SCHEDULE 13G - TO BE INCLUDED IN STATEMENTS  
FILED PURSUANT TO RULE 13d-1(b) or 13d-2(b)  
  
	Pursuant to the instructions in Item 7 of Schedule 13G, Fidelity  
Management & Research Company ("Fidelity"), 82 Devonshire Street, Boston,  
Massachusetts 02109, a wholly-owned subsidiary of FMR Corp. and an investment  
adviser registered under Section 203 of the Investment Advisers Act of 1940,  
is the beneficial owner of 6,130,323 shares or 8.87% of the common stock  
outstanding of Unifi Incorporated ("the Company") as a result of acting as  
investment adviser to several investment companies registered under Section 8  
of the Investment Company Act of 1940.  The number of shares of common stock  
of Unifi Incorporated owned by the investment companies at May 31, 1995  
included 824,473 shares of common stock resulting from the assumed conversion  
of $24,460,000 principal amount of 6% Convertible Subordinated Debentures  
(33.70799 shares of common stock for each $1,000 principal amount of  
debenture).  
  
	Edward C. Johnson 3d, FMR Corp., through its control of Fidelity, and 
the  
Funds each has sole power to dispose of the 6,130,323 shares owned by the  
Funds.  
  
	Neither FMR Corp. nor Edward C. Johnson 3d, Chairman of FMR Corp., has  
the sole power to vote or direct the voting of the shares owned directly by  
the Fidelity Funds, which power resides with the Funds' Boards of Trustees.   
Fidelity carries out the voting of the shares under written guidelines  
established by the Funds' Boards of Trustees.  
  
	Fidelity Management Trust Company, 82 Devonshire Street, Boston,  
Massachusetts 02109, a wholly-owned subsidiary of FMR Corp. and a bank as  
defined in Section 3(a)(6) of the Securities Exchange Act of 1934, is the  
beneficial owner of 604,958 shares or 0.88% of the common stock outstanding of  
the Company as a result of its serving as investment manager of the  
institutional account(s).  The number of shares of common stock of Unifi  
Incorporated owned by the institutional account(s) at May 31, 1995 included  
95,728 shares of common stock resulting from the assumed conversion of  
$2,090,000 principal amount of the 6% Convertible Subordinated Debentures  
described above.  
  
	Edward C. Johnson 3d and FMR Corp., through its control of Fidelity  
Management Trust Company, has sole dispositive power over 604,958 shares and  
sole power to vote or to direct the voting of 399,600 shares, and no power to  
vote or to direct the voting of 205,358 Shares of common stock owned by the  
institutional account(s) as reported above.  
  
	Edward C. Johnson 3d and Abigail P. Johnson each own 24.9% of the  
outstanding voting common stock of FMR Corp.  Mr. Johnson 3d is Chairman of  
FMR Corp.  Various Johnson family members and trusts for the benefit of  
Johnson family members own FMR Corp. voting common stock.  These Johnson  
family members, through their ownership of voting common stock and the  
execution of a family shareholders' voting agreement, form a controlling group  
with respect to FMR Corp.  
  
 
 
SCHEDULE 13G - TO BE INCLUDED IN STATEMENTS  
FILED PURSUANT TO RULE 13d-1(b) or 13d-2(b)  
  
RULE 13d-1(f)(1)  AGREEMENT  
  
	The undersigned persons, on June 9, 1995, agree and consent to the joint  
filing on their behalf of this Schedule 13G in connection with their  
beneficial ownership of the common stock of Unifi Incorporated at May 31,  
1995.  
  
	FMR Corp.  
	By	/s/Arthur S. Loring  
Arthur S. Loring 
Vice President - Legal  
	Edward C. Johnson 3d  
	By	/s/Arthur S. Loring  
Arthur S. Loring 
Under Power of Attorney dated  
5/17/89 
On File with Schedule 13G for 
Airborne Freight Corp. 9/10/91  
	Fidelity Management & Research Company  
	By	/s/Arthur S. Loring  
Arthur S. Loring 
Sr. V.P. and General Counsel