Metro Bank is now giving customers the option to choose a non-binary prefix "Mx" on forms.
The lender said the option will be available to customers opening products like current accounts, as well as to staff.
It made the change off the back of feedback from staff and customers, and said its relatively new status enabled it to react quickly.
A Scottish teenager told Buzzfeed earlier this year they couldn't open a bank account as they don't identify as male or female.
Metro Bank's chief people officer Danny Harmer told Buzzfeed: "Once you realise this is an issue [you notice that] every single thing you pick up says, 'Title: Mr or Mrs'. And then the next question is: 'Gender:male or female.'"
He added that Metro Bank tried to listen. "Sometimes there are issues that are too difficult to do something about, but this one was definitely not one of them."
"I think a lot of organisations get tied up in finding reasons not to do things and worrying about how it might be misinterpreted."
Other firms like the Royal Bank of Scotland have also made the step of allowing customers to opt for Mx rather than Ms, Mr and Mrs. Facebook provides the option of selecting a gender other than male or female, and users can pick a pronoun from he, she or they.
A spokesperson for LGBT lobby group Stonewall said: "The changes that Metro Bank has made to its forms give important and much-needed recognition to people who do not identify as either male or female. It's great to see them taking proactive steps to ensure their needs are met and that they are accepted and included."
Last year, the Oxford Dictionaries website added the Mx honorific: "a title used before a person's surname or full name by those who wish to avoid specifying their gender or by those who prefer not to identify themselves as male or female."