In this paper, the p-moment stability of impulsive differential equations is considered. A theory about this problem under a weak condition and an assumption which is more familiar in impulsive system is proved. As an application, the impulsive synchronization of Lorenz system excited by white-noise is considered, the p-moment stability of error system is proved, so the synchronization can be realized using impulsive method under p-moment stability. Numerical simulation verify the feasibility of this synchronization method.