  How to accurately solve time-dependent Schr\"odinger equation is an
interesting and important problem. Here, we propose a novel method to obtain
the exact Floquet solutions of the Schr\"odinger equation for periodically
driven systems by using Floquet theorem and a time-dependent unitary
transformation. Using the method, we give out the exact Floquet solutions of
wave function for three interesting physical models -- linear potential model,
harmonic oscillator model, and the coupled harmonic oscillator model in the
presence of a periodic driving. In addition to the quasienergy, we also give
out the analytic expression of Berry phase for the harmonic oscillator model.
Moreover, the idea presented in this paper can be used in mathematics to solve
partial differential equations.
