Apple posted revenues of $13.5bn in the three months to 27 March, up from $9.1bn the previous year.
Profits increased from $1.6bn to $3bn in the period, largely driven by a 131% year-on-year increase in the number of iPhones sold to 8.75 million during the quarter.
Steve Jobs, Apple chief executive, said: "We've launched our revolutionary new iPad and users are loving it, and we have several more extraordinary products in the pipeline this year."
Among the new launches is a new version of the iPhone which will be on sale from June this year.
The results beat analyst forecasts, and were declared by Jobs to be "the best non-holiday quarter ever".
The number of iPods sold fell by 1% on the year to 10.89 million, though this was compensated for the leap in demand for the iPhone, which proved particularly popular in Asia and Europe.
The rise in demand for the iPhone has been aided by deals with new mobile network providers, including Vodafone in Britain.
Earlier this month, Apple said it was delaying the launch of its iPad in the UK until the end of May due to high levels of demand in the US.