The images, taken by Syd Shelton, from Pontefract, include pictures of The Clash, Misty in Roots and The Specials.
The collection also features photos taken at the Rock Against Racism Carnival at Victoria Park, Hackney, which attracted a crowd of 100,000.
The show runs from Friday to 3 September at the Impression Gallery.
The Rock Against Racism (RAR) movement formed in response to controversial remarks made by Eric Clapton in 1976.
In the following years, RAR staged marches, festivals and more than 500 concerts in the UK in a bid to fight racism through music.
Shelton, who studied Fine Art in Leeds and Wakefield, said he became involved with the movement after returning to the UK from America in 1976.
He said: "I was appalled at the state of race relations in Britain, in particular things like the Black and White Minstrel Show and the signs I saw in some windows saying 'No Blacks, No Dogs, No Irish'.
"It was a pretty serious situation and I always loved music and very quickly hooked up with the people that had set up RAR.
"It was a bizarre mixture of people, photographers, graphic designers, writers, actors and, of course, musicians.
"We were very lucky in the sense that we tuned in to that explosion of punk and UK reggae and brought the two together. That said more about what RAR was about than any of the slogans we may have shouted from the stage."
He added: "I hope the exhibition shows that you can change things and you can actually take a stand, even in the most difficult of situations.
"If it inspires people to be photographers that would be great but I hope it will also inspire people to fight against racism and inequality."

Konrad, 38, swam the equivalent of 290 lengths of an Olympic-size swimming pool after his 36-foot boat, which was on auto pilot, drifted away from him off the South Florida coast.
The United States Coast Guard reported that friends became concerned when he failed to return for dinner.
After up to 12 hours in the water, he had treatment for hypothermia symptoms.
He played 82 games for the Dolphins between 1999-2004.

The 24-hour Underground service was originally scheduled for September, but was delayed over a dispute about pay and conditions.
Following the breakdown of talks on Wednesday, union leaders said the launch would not happen this year.
But during a trip to Japan Mr Johnson said: "We are going to have a Night Tube eventually."
He had previously said he was "relaxed" about when the service was introduced, as long as it happened before the end of autumn.
Mr Johnson said during a business visit to Japan: "We'll do a Night Tube and obviously I hope very much that the offer on the table, which is a very good one, is now communicated properly to the workforce of London Underground and I think we should just get on with it.
"We've done without it for 150 years and I'm sure we can rub along a little bit longe,r but we are going to have a Night Tube eventually."
Unions took industrial action during the summer having called for increased pay and a limit on how many all-night shifts their members would be asked to do.
As negotiations between the unions and London Underground came to a halt,  Finn Brennan from drivers' union Aslef, said discussions had broken up because LU management had "mishandled" the process.
Photographs capturing some of the most important moments and inspirational figures of the Rock Against Racism movement are to go on show in Bradford.
[NEXT_CONCEPT]
Former Miami Dolphins running back Rob Konrad swam nine miles to shore after falling off his boat while fishing.
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London mayor Boris Johnson has backed away from a timetable for the opening of the city's Night Tube.