This paper aims to investigate an asymmetric bistable system driven by non-Gaussian Lvy noise. The stationary probability density functions are obtained by the Grnwald-Letnikov scheme, and the effects of noise intensity and stability index on the stationary probability density are examined. Phase transitions can be observed though a qualitative change of the stationary probability distribution, which indicates that the phase transitions are induced by the asymmetric parameter and the stability index of Lvy noise. Additionally, the mean first passage time is considered, and different mechanisms for the effects of asymmetric parameter, noise intensity and stability index on first passage time are also obtained.