However, a Jamaican LGB organisation has said the campaign will damage their cause as one of the products targeted, Red Stripe beer, is openly supporting the anti-hate movement.
A campaign website, http://www.boycottjamaica.org/ was set up by former Human Rights Council Spokesman Wayne Besen, along with prominent LGB rights activists Jim Burroway and Michael Petrelis, and campaigns for Jamaica to become a pariah state until social attitudes on the island towards homosexuality change.
Jamaica is considered to be one of the most homophobic countries in the world, where gay sex between two men can carry a ten-year jail sentence or hard labour. Sex between two women is currently legal.
Mr Besen told the Huffington Post: "Why boycott [Jamaica]? Because Jamaica is on a downward spiral and suffers from collective cultural dementia on this issue. There is clearly a pathological panic and homo-hysteria that has infected this nation at its core.
"Jamaica is an island of self-righteous hypocrites. The Bible is used to rationalise brutality, and vigilante violence is justified with talk of virtues and values. But, the island is quite comfortable with ganja and gratuitous sex for heterosexuals."
The website calls for boycotting of specific of Jamaican products sold in the US, including Myers Rum and Red Stripe beer.
In an open newsletter, the Jamaica Forum for Lesbians All-Sexuals and Gays (J-FLAG) responded to the website's demands:
" … we find it unfortunate that a campaign has been launched calling for the boycott of two Jamaican products, one marketed by a company that unequivocally distanced itself from the hostility and violence typical of Jamaican music towards members of the LGBT community.
"In April 2008, Red Stripe took the brave and principled stance to cease sponsorship of music festivals that promoted hate and intolerance, including that against members of the LGBT community.
"The naming of Red Stripe, therefore, as a target of this boycott is extremely damaging to the cause of LGBT activists in Jamaica.
The letter added: "Jamaica’s deeply ingrained antipathy towards homosexuality and homosexuals is a social phenomenon that will not be undone by boycott campaigns or government dictate. It requires the painstaking effort of confronting the society and talking to social actors who can bring change in the way society sees LGBT people."
Last month, it was revealed that gay men in Jamaica were at a higher risk of contracting HIV due to discrimination.
The prime minister of Jamaica, Bruce Golding, also recapitulated his government's attitude towards homosexuality:
"We are not going to yield to the pressure, whether that pressure comes from individual organisations, individuals, whether that pressure comes from foreign governments or groups of countries, to liberalise the laws as it relates to buggery," he said.