Performing Bayesian inference via MCMC can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of PDEs. One strategy is to replace the forward model with a low-cost surrogate model; however, simply replacing the high-fidelity model with a low-fidelity model can lead to a lower approximation quality result. In this talk, we seek to address this challenge by introducing an adaptive procedure to construct a multi-fidelity polynomial chaos（PC）surrogate and explore the posterior simultaneously. More precisely, the new strategy starts with a low-fidelity surrogate model, and this surrogate will be adaptively corrected using online high-fidelity data. The key idea is to speed up the MCMC by combing, instead of replacing, the high-fidelity model with the low-fidelity model. We also introduce a multi-fidelity surrogate based on the deep Neural Networks to deal with problems with high dimensional parameters. Numerical experiments confirm that the proposed approach can obtain accurate posterior information with a limited number of forward simulations.