The employment reduction will be split between the bank’s UK and non-UK locations.
The cuts are part of a reorganisation a of its investment bank.
The bank has already shed some 30,000 employees over the past two years, 22,000 of them in the UK.
RBS said the restructuring was also designed to prepare the bank for new UK regulatory requirements for banks to ring-fence their core UK operations from their riskier investment banking activities.
Markets took the statement well as RBS’ share prices rose 2.9% in early trading, outperforming other large companies on the FTSE 100 index.
The bank is now 82%-owned by the UK government after taxpayers injected £45.5bn of new capital into RBS.
Stephen Hester, group chief executive, said: “...for our strategy to be effective, it must adjust to fresh challenges. And it is clear that, particularly in the wholesale banking arena, significant new pressures have emerged.
“The changes we are announcing today seek to ensure that RBS is at the front of the pack in pursuing a strategy that reflects the environment we expect to operate in.
“Our goal from these changes is to be more focussed for customers, more conservatively funded, more efficient and with better, more stable returns for shareholders overall.”