The Facebook group Jews for Jeremy has almost 300 members. Its founders say it was launched in response to "unscrupulous" attacks from the media.
"Some members of the group live in Jeremy Corbyn's constituency, some have worked with him on various campaigns, and many know him from his reputation and his tireless work for the disadvantaged in society, including migrants and asylum seekers," JfJ said in a statement.
It added: "Members applaud his efforts to bring together opposing parties to many conflicts in dialogue in a constructive way, and are dismayed that in some cases this has been held against him."
Supporter Rhea Wolfson, 25, said Mr Corbyn "offers something different", and "best reflects" her values as a Labour member. A former outreach manager for the New Israel Fund - a liberal Zionist group that fundraises for social justice initiatives - she said that he was "breathing life back into the party".
She added: "To me, the Labour Party isn't about being a bit left-wing or a bit into social justice - it's about links with trade unions and links to socialist ideals. Jeremy Corbyn reflects that."
She said she had been swayed by Mr Corbyn's "straight-talking" approach to politics.
Ms Wolfson is a London Young Labour Executive member and has spent time campaigning for the Islington North MP in the capital and in Scotland. She said: "He is the only candidate to be uncompromisingly anti-austerity, and he has economists behind his plans."
A former president of Oxford University's Jewish and Israel societies, and an ex-chair of the Zionist Youth Council, she was untroubled by Mr Corbyn's positions on Israel - although she disagreed with his boycott stance. She said: "He has said time and again he doesn't agree with the views of Hamas and Hizbollah, and I think certain members of our community have used his connections to make a political point.
"I've have no doubt in my mind that he might have made mistakes in sharing platforms with people, but there isn't anything he believes that isn't compatible with my views on Israel or Judaism."
She said she herself had faced criticism from Jewish community figures for her decision to back Mr Corbyn. "I've been stunned at how rude and childish some of the more senior people have been when I've expressed my views on Facebook," Ms Wolfson said.
Jenifer Izaakson, a former intern at Jewish Council for Racial Equality, said she had registered to vote in the election and had intended to back Mr Corbyn because he "seemed very thoughtful and is fundamentally more trustworthy than most politicians".
His appeal lies, she said, in "policies that will give young people and the less well-off a stake in society again. The best for me is the mass building of social housing. I want to have a family one day, but I worry that in London I couldn't even get a council home."
The four candidates' views of Israel were not a priority, she said. But she added that Mr Corbyn needed to be more careful about his associates.
"I think the responsibility is on him and he should, once leader, employ staff who do greater research about who he might be dealing with or speaking alongside."
She added: "I think beyond simply opposing all forms of racism, it would be a good idea for him once Labour leader to develop a policy that specifically outlines how to address antisemitism.
"Consulting Jewish groups to do this could help."
Kery Lambeth, a 29-year-old constituent of Mr Corbyn, backs him because of his work in her neighbourhood. She said: "I've always rated him as an MP. Personally he helped me chase up my passport application after I was granted citizenship. I think he is expressing things around economics, social justice and anti-austerity that people broadly agree with."
Another Jewish constituent, Reuven Davidson, said he did not believe Mr Corbyn held the same views as some of the antisemites and Holocaust deniers that he had been criticised for meeting.
