The profits figure, which was adjusted to exclude goodwill and other one-off items relating to the acquisition and integration of Arco and Burmah Castrol, is 52% higher than the same period a year earlier.
The profits figures means BP, the UK's largest by stock market capitalisation, was making about £1.3m an hour, or £355 a second.
BP said that soaring US prices for natural gas, helped power the profits rise.
Production was at record levels and up 13% on a year ago, the company said.
But BP's UK-based petrol retail business reported a £14.6m ($20.1m) loss in the first quarter of this year.
"The trading environment remains broadly positive, in spite of the slowdown in the world economy," said BP chief executive Sir John Browne.
Oil giants 'profiteering'
Last week, BP's rival Royal Dutch/Shell reported a 23% rise in net profit to £2.69bn ($3.86bn) for the first three months of 2001.
The string of record profits from oil companies in recent months has led some consumer groups to accuse them of profiteering.
They come less than a fortnight after the price of petrol in the UK was increased, and at a time when petrol prices in the US are at record levels.
Both BP and Shell have faced calls that they should be subject to a windfall tax on profits, but so far the UK Chancellor Gordon Brown has put the issue on a back-burner.
The record rise in profits still was not enough to satisfy the markets.
BP shares were down 14.5p at 596.5p in mid-afternoon trade.