The charity said Andrew Frost was preaching on the streets of Nottingham city centre in March. He preached on the consequences of sin, and quoted Luke 13:1-5 and Matthew 15:19.
According to Christian Concern, as he preached, two men holding hands and in a homosexual relationship walked by. Rory Green, a friend of Frost who was preaching alongside him at the time, reported that the two men shouted abusive comments at Frost. Frost continued to preach from Scripture.
The organisation said that the two men left, but approximately 15 minutes later a woman, who said she was the mother of one of the men, approached Frost, and accused him of abusing her son and his partner. One of the men then returned and called the police.
The two men claimed that Andrew verbally abused them and directed several lewd comments at them, all of which Frost denied.
Frost was charged under the Public Order Act 1986, "with intent to cause harassment, alarm or distress used threatening, abusive or insulting words or behaviour."
After hearing all the evidence at Nottingham Magistrate's Court last week, Frost was found not guilty.
During the hearing last week, the court heard evidence from Frost, Green and four character witnesses, all of whom were shocked at the allegation that Frost had faced, according to Christian Concern.
Frost added that he has been approached by people in same-sex relationships before, and each time reassures them that he has nothing against them.
He said: "I am thankful that the judge saw sense and acquitted me of this charge.
"Christians need to be free to share the good news of the gospel to anyone who will listen – as we are commanded in Scripture to do."
Green commented: "We are law abiding citizens. We love God and love people. We never seek to intentionally hurt people nor cause; alarm, distress and harassment. If anything that day; the two males, their mother and male partner caused us intentional alarm distress and harassment. We deescalated appropriately and wanted to sort this out properly as we did not want them to think we hate them. "
He added: "Andrew is a good man and loves people. He wants to see people know Jesus. Andy loves all people, from all walks."
Andrea Williams, chief executive of the Christian Legal Centre which is supporting Frost, said: "We are delighted with this result.
"The freedoms that we enjoy today in this nation are largely due to our biblical foundation, yet the freedom to preach from this very Bible is under increasing threat.
"At the Christian Legal Centre we are seeing an increasing number of street preachers arrested for preaching the gospel.
"This encouraging result should offer some reassurance to Christians who may feel fearful of the consequences of sharing their beliefs with others."