Core pretax profit rose to 2.36 billion pounds (USD 3.11 billion) from 1.98 billion pounds a year earlier, the London-based bank said.
Barclays' core businesses include those it plans to continue operating after it sheds riskier assets and focuses on Britain. Net income for the entire company fell 41 percent to 677 million pounds.
"The picture in the second quarter is one of strong and accelerating progress against our strategy," CEO Jes Staley said in a statement. "We remain confident that it is the right plan for Barclays, and see no reason to adjust it, or the pace of delivery, in light of the vote by the UK last month to exit the EU."
Staley said the bank is dealing with legacy issues for past misconduct. Litigation and conduct costs fell by almost 50 per cent to 420 million pounds.
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The figures come a day after another London-based bank, Lloyds, announced it was cutting jobs and shuttering branches the first big layoffs since the EU referendum in June. Lloyds said changing consumer behaviour and the move to digital banking were behind its decision.
In a conference call after the results, Staley said that he believed a single market for financial services remained the best option for the economy, but said the bank was prepared if necessary to "adapt our operations to maintain our access to Europe."
"We do not currently see a need in our options to shift jobs or significant operations elsewhere," he said. "If we do require a build-up of capability in another EU jurisdiction as part of our plans, then we can do so, and we will."
Barclays took strides to insulate itself from the impact of the Brexit vote, but Staley sidestepped a question on whether the bank considered the potential of a Donald Trump US presidency a possible shock to the economy.
"It could be an interesting fall," he said. "On a personal level, I think the world has achieved a degree of geopolitical stability on the back of economic integration and I hope we continue down that path.