Brighton will be the first UK city to demand that music retailers ban reggae and rap albums with "anti-gay" lyrics.
Councillors want stores to boycott artists including Elephant Man
Brighton and Hove City Council voted unanimously on Thursday to write to the managing directors of its three largest stores condemning the music.
It urged them not to stock artists such as Buju Banton, Beenie Man, Elephant Man, TOK, Vybz and Bounty Killer.
The Green Party, which put forward the motion, said the music "incites the murder of lesbians and gay men".
Green councillor Simon Williams, who tabled the motion, said: "This unanimous vote by all parties in the council is a significant victory in the long battle against murder and hate music.
He admitted the council did not have the power to force the three stores - Virgin Megasotre, HMV and MVC - not to sell the music.
But he said the vote "sends retailers a very strong message that Brighton and Hove cares deeply about this issue".
The council said that Brighton and Hove has one of the largest lesbian, gay, bisexual and transgender communities in the country.
It also told public entertainment licence holders that the council was against such music being played.
And it is to ask the city's three MPs to lobby the government to extend anti-incitement to hatred legislation to include the lesbian and gay community.
'Happy to comply'
A spokesman for HMV said the records were not on display in Brighton and would only be sold to over-18s if they were particularly requested.
He added the company would consider a request from the council and backed any attempt to amend legislation.
"That way retailers would have a strong set of guidelines," he said.
MVC's Brighton branch does not display "anti-gay" albums.
Manager Daniel Shaw said he would be happy to comply with a request for a ban but the final decision rested with his head office.
A spokeswoman there said: "While there is no law to prevent the sale of this material we don't feel that we can censor it, although we are aware that Brighton is a special case."
A spokesman for Virgin megastore said it would "seriously consider" the request to stop selling certain albums.