[BBC] – Pastor Steven Anderson, who is based in Arizona, runs the Faithful Word Baptist Church which says that homosexuality is an abomination and should be punishable by death.
Officials said his statements were “not conducive to the current climate”.
Mr Anderson has been barred from South Africa and deported from Botswana.
The pastor had planned to travel to Jamaica with his 14-year-old son to carry out “missionary work” when he was prevented by airline officials from boarding the plane on Monday.
“I had a connecting flight in Atlanta, so as soon as I got to Atlanta, Delta Air Lines told me that they received a notification from Jamaica that I was not going to be allowed to enter,” Mr Anderson told The Gleaner newspaper.
“I was kind of surprised that Jamaica would ban me for my views on homosexuality,” he added.
Jamaica has laws criminalising gay sex and rights groups have warned that LGBT (lesbian, gay, bisexual and transgender) people face frequent discrimination.
But LGBT rights activists in Jamaica started a petition asking the Jamaican government to ban Mr Anderson and it was signed by more than 38,000 people.
Jay John, who launched the petition, said he was very pleased by the outcome and called it a “victory”.
“His literal interpretation of the Bible regarding killing of gay people should not be echoed in a society like Jamaica,” Mr John had argued.
In September 2016, Mr Anderson was deported from Botswana after he said on a local radio programme that homosexuals should be “stoned to death”.
A week earlier, he had been banned from South Africa, and before that, from the UK.
