The plans form part of an overhaul which CEO Antony Jenkins hopes will convince a sceptical public that he will change a bank which has been dogged by a series of scandals, including a $450 million fine for rigging interbank lending rates or Libor.
"Believe me, I understand the cynics and the sceptics out there, but cynics and sceptics never built anything. It will take years before people actually change their impression of us. I'm not daunted by that at all," Jenkins told BBC radio.
Barclays also unveiled plans to pay its investment bankers an average bonus of 54,100 pounds, down 17 percent on the year before. Bonuses across the bank will total 1.85 billion pounds, down 14 percent on the year.
Jenkins said the job cuts will include 1,800 in corporate and investment banking and 1,900 in its European retail and business banking.
He plans to focus investment in Britain, the United States and Africa, and cut its presence across continental Europe and Asia.
That will include a scaling back of the investment bank's equities and advisory businesses in continental Europe and Asia.
Jenkins said he aimed to cut the bank's cost base to 16.8 billion pounds in 2015, excluding one-off costs of 2.7 billion over the next three years.
Unveiling the strategic plan alongside annual results, the bank reported a yearly pretax profit of just 246 million pounds, down from 5.9 billion in 2011 due to charges for compensating customers mis-sold products and a loss on the value of its own debt.
However, the bank said its adjusted pretax profit for 2012 was 7.05 billion pounds, up 26 percent on the year and in line with the average forecast by analysts.
Pretax profit at the investment bank rose by 37 percent to 4.1 billion pounds.
Shares in Barclays opened up 0.2 percent.
Copyright: Thomson Reuters 2013