Markov Chain Monte Carlo method is a universal-used method in numerical integration. In this talk, we will discuss the dynamic weighting MCMC proposed by Wong and Liang (1997), which makes the Markov chain converges faster. In the decades, Metropolis Hasting algorithm is an important simulation method, but there are still some drawbacks in the simulation. For example, the movement of the process can be influenced by some tiny probability nodes. This phenomenon may directly affect to our simulated estimation. Our main work is to review the weighted MCMC and give some theoretical proof in some special cases. Through the manner, we can make the MCMC method more efficient.