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.
Co-operative Bank is cutting 200 jobs as it looks to continue its recovery.