Staff have been told the posts will go by March and will mainly affect management and head office roles in Manchester and Stockport.
Deputy chief executive Liam Coleman said the cost reductions were "critical" as it continues its three-year plan to rebuild the business.
The bank almost collapsed in 2013 and it expects to continue to be loss-making until the end of next year.
Mr Coleman said: "These cost reductions are critical to progressing our turnaround and delivering a cost base which supports a sustainable core bank."
He said it would continue to consult colleagues and trade unions on the proposals over the coming weeks.
"We have made progress in turning the bank around since 2013, but have always been clear that the bank's recovery is a difficult journey."
He said the business would not make a profit this year or next year while it continues its "turnaround plan in a challenging economic environment".
Rob MacGregor, national officer at trade union Unite, said: "The speed and breadth of these cuts will hit the Co-operative Bank's much cherished customer service and with it the bank's unique selling point.
"Compulsory redundancies are anathema to all trade unions, but the timing of this exercise just before Christmas is a real blow to our members."
He said the union would be supporting members and pressing the bank to reconsider the cuts where possible.
The bank was owned by the Co-operative Group until 2013, when a Â£1.5bn hole was discovered in its finances.
The group had to go to outside investors to support the Co-op Bank, which is now 80% owned by US hedge funds, with the remainder held by the Co-op Group.

The show asked whether rape was ever a woman's fault.
The poll followed on from comments The Pretenders' singer Chrissie Hynde had made in the Sunday Times.
She said she blamed herself for a sexual assault she had experienced aged 21 and was criticised when she said women "have to take responsibility".
The Loose Women poll drew criticism on Twitter, with one viewer Rebecca Gill calling it "off the scale of acceptability".
Rape Crisis for England and Wales tweeted that it was "not an appropriate opinion poll; legally and morally the answer is a resounding 'no'" and questioned whether the show would "have a poll on whether it is ever someone's own fault if they are mugged or murdered?"
Katie Russell the national spokesperson for Rape Crisis England & Wales added:
"A programme like Loose Women could choose to use its high profile to raise awareness and understanding of rape, its impacts and prevalence, and to support and encourage survivors to seek services like those Rape Crisis offers; instead, they've reinforced myths and stereotypes with this ill-considered, insensitive and insulting poll."
Peterborough Rape Crisis Care Group called the poll "harmful to women".
In a statement issued to The Guardian an ITV spokesperson admitted the poll "was misjudged".
"Loose Women is a daily talk show centred around topical debate and this discussion, linked to a recent news story, involved a full and frank range of views from the panellists.
"We always want to know what our viewers think about topical issues, however, we accept that the wording of the online poll was misjudged and we apologise for any offence caused."
Broadcasting watchdog Ofcom said it had received 53 complaints about the poll and will "assess these complaints before deciding whether to investigate or not".
Last year, Judy Finnigan apologised for comments she made on Loose Women about rape.
She upset viewers when she talked about convicted rapist Ched Evans and said the rape was "not violent".
"I apologise unreservedly for any offence that I may have caused as a result of the wording I used," said the former This Morning presenter.
Co-operative Bank is cutting 200 jobs as it looks to continue its recovery.
[NEXT_CONCEPT]
ITV has apologised after a poll on Loose Women about rape offended viewers.