Net profits of $6bn (£3.7bn) were reported by the company, whose revenues for the quarter were $26.74bn.
During the quarter 4.13m Macs, 16.4m iPhones, 7.33m iPads and 9.45m iPods were sold by the company, with 62% of revenue coming from outside the US.
Chief operating officer Tim Cook, who is standing in for chief executive Steve Jobs whilst Mr Jobs is on open-ended medical leave, has emphasised the company's continuing ambition for further growth.
In a statement, Mr Jobs said ""We had a phenomenal holiday quarter, with record Mac, iPhone and iPad sales. We are firing on all cylinders and we've got some exciting things in the pipeline for this year, including iPhone 4 on Verizon."
Concerns have been voiced about the impact of Mr Job's absence on the company's future.
News of Apple chief executive's latest health problems, and his decision to begin another period of medical leave, were announced on a US public holiday.
The news was reflected in a drop in shares when the markets reopened; shares closed down 2.2%.