But another research firm, IDC, disagrees, saying HP is still on top, by a narrow margin.
The firms agree that the global PC market shrank in the third quarter by more than 8 percent from last year.
Consumers are holding off as they await the launch of Microsoft's new operating system, Windows 8, on Oct. 26.
Lenovo vaulted onto the international scene when it bought IBM's PC division in 2005. It's been the No. 2 PC maker in the world for a few years, behind Hewlett-Packard Co.
(Copyright 2012 by The Associated Press. All Rights Reserved.)