[en] Highlights: • Novel strategy to sample from multi-modal distributions. • Creative method to calculate the unknown integration constant. • A whole scheme for realizing the sampling of zero-variance importance function and getting the integration constant. A general purpose strategy is proposed to realize asymptotically the zero-variance importance sampling. The unknown integration constant can also be calculated simultaneously. This strategy can sample efficiently from multi-dimensional zero-variance importance function which is multi-modal by particular Markov Chain random walk. Sampling from this kind of distribution has been a challenge for a long time. Moreover, by using the probability density function reconstruction method, the unknown integration constant can be estimated. This feature is absent in traditional Markov Chain Monte Carlo method. Some multi-dimensional integrals are analyzed carefully. The results show this strategy is efficient.