Pre-tax income rose by 15 per cent year-on-year to $8.4bn (£5.8bn), with net income rising 30 per cent to a record $6.9bn, the bank said.
Earnings per share rose by 38 per cent to $0.62, above the $0.59 predicted by analysts according to consensus expectations. Return on equity for average shareholders was 10.8 per cent.
Net interest income rose by $550m thanks to "benefits from higher interest rates". The bank's equities and asset management divisions were behind a three per cent increase in non-interest income to $11.5bn.
Why it's interesting
Economists and investors have been looking to Wall Street earnings to deliver them from the doldrums of trade war fears and equity market volatility. The big banks have given it their best shot so far, with BAML adding to profit rises at JP Morgan Chase, Citigroup and Wells Fargo.
The banks have benefited from strong economic growth in their home market and a pick-up in world trade, while higher interest rates from the Federal Reserve have improved margins on lending.
However, BAML's trading division failed to capitalise on increased volatility on global markets in the first quarter which was expected to boost profits. Fixed income, currencies and commodities sales and trading revenues fell by 13 per cent, with BAML blaming "lower activity and less favorable marketsin credit-related products".
Meanwhile, investment banking fees fell by 15 per cent to $1.4bn for the quarter compared to a strong period last year.
What Bank of America said
Brian Moynihan, BAML's chief executive, said: "Our responsible growth model continues to deliver consistent results. Strong client activity, coupled with a growing global economy and solid US consumer activity, led to record quarterly earnings.
We grew loans in our business segments by $45bn and increased deposits by $41bn. We continue to invest in new capabilities in our mobile banking app, the expansion and renovation of our financial centres, and the hiring of additional client relationship professionals.
He added: "We believe these investments, and our focus on operational excellence, will drive sustainable growth over time.”