The potential-energy-surface crossings between different electronic state widely exist in photophysics, photochemisty and photobiology.At the crossing regions, the strong nonadiabatic couplings induce the ultrafast nonadiabatic transitions that play essential roles in many important photoinduced reactions.The simulation of such nonadiabatic dynamics represents a great challenging since the Born-Oppenheimer approximation breaks down and a consistent treatment should be developed in the description of the coupled electron-nucleus motions.