This article formulates and studies a model of Hybrid Impulsive and Switching Stochastic Systems (HISSS). Using integral Inequality、Ito Isometry、The Gronwall Inequality、Doob’s martingale Inequality and Borel-Cantelli Lemma, we has got a existing and unique result for HISSS. On the other hand, to the best of author’s knowledge, date up to now, seldom stability result has been arrived for HISSS. In order to fill this gap, p—moment asymptotic stability and p—moment exponential stability are considered. Some theorems on p—moment asymptotic stability and p—moment exponential stability of HISSS are established by using Lyapunov-Krasovskii function and stochastic analysis theory.