Britain's second-largest bank says it is seeking to make the cuts through voluntary buy-outs. It currently employs 33,600 people at 1,577 branches in Britain.
Barclays said "the way in which our customers access their banking services is changing rapidly," with people using computers and smartphones for everyday banking and paying fewer visits to branches.
The bank said in a statement Thursday that "as a result of technological changes, we will be able to provide better service for our customers with fewer staff."
The Unite trade union called the job cuts among cashiers, branch managers and other staff "a colossal mistake."