The phase transition and stochastic resonance (SR) induced by Lévy noise in a duffing system were examined, and the influences of noise intensity and stability index of Lévy noise on SR were analyzed. The results imply that smaller damping parameter is more beneficial to the observation of SR, and the decrease of stability index weakens the occurrence of the SR. Furthermore, the stationary probability densities functions of the system were obtained by using Monte Carlo method. It's found that the skewness parameter noise intensity and stability index can induce the phase transition, and the mechanism of the action of Gaussian noise and Lévy noise is different.