The Co-operative Bank asked Christian Voice to close the account it had held for three years, saying the group's opinions were incompatible with its support for diversity.
Christian Voice said the bank was discriminating against it on religious grounds. National Director Stephen Green said, "The Co-op bank, for all its fine words, is discriminating against us on the grounds of conscience and religion."
He said he was now expecting the bank to bar other Muslim, Christian and Jewish groups that they all shared the same view on homosexuality.
However a spokesman for the bank stressed the decision was based "purely on the issue of diversity" and not "on the grounds of religion."
"It has come to the bank's attention that Christian Voice is engaged in discriminatory pronouncements based on the grounds of sexual orientation," the spokesman said.
"This public stance is incompatible with the position of the Co-operative Bank, which publicly supports diversity and dignity in all its forms for our staff, customers and other stakeholders."