In this paper, the Lévy noise-induced transition in an underdamped asymmetric bistable system is discussed. Lévy noise is generated through the Janicki-Weron algorithm and the numerical solutions of system equation is obtained by the fourth-order Runge-Kutta method. Then the stationary probability density functions are obtained by solving the equation of system. The influence of the damped coefficient γ, asymmetric parameter r of system, stability index α, skewness parameters β and noise intensity D on the stationary probability density are analyzed. The numerical simulation results show that the asymmetric parameter r, stability index α, skewness parameters β and noise intensity D can induce the phase transition. However, the phase transition cannot be induced by the damped coefficient γ.