Here we report our study on the lithium-doped ZnO films prepared by sol-gel method. The films are polycrystalline wurtzite structure and the average particle size is about 50 nm. All the films are ferromagnetic, and the film with Li content of 8 at. % has the largest saturation magnetization of about 55 memu/g. The photoluminescence spectra show that the films have weak emission near ultraviolet region and strong emission in visible regions. The Li atoms in Zn sites can induce Zn vacancies and a low acceptor level in the energy gap, which are required for ferromagnetism. The first-principles calculations demonstrate that the ferromagnetism in the Li-doped ZnO originates from the induced magnetic moment of oxygen atoms in the nearest neighbor sites to Li-Zn vacancy pair.