<p>In this paper, we study a stochastic hepatitis B system with incomplete immunity and vaccination. Firstly, we show the existence of a global positive solution of the system and then give a sufficient condition for eradication of hepatitis B. By constructing a Lyapunov function we obtain a sufficient condition for the existence and uniqueness of an ergodic stationary distribution to the system. We give some numerical simulation examples to verify the theoretical result. Conclusions suggest that smaller transmission rate of HBV, effective treatment measures, and larger-scale vaccination are beneficial for controlling the prevalence of hepatitis B. In addition, larger noise intensity of environment is also favorable for elimination of hepatitis B.</p>