An automatic determination method for the convergence and required posterior samples is proposed to address the problem that the multi-chain MCMC algorithm mainly relies on setting a large number of iteration steps to generate a sufficient number of posterior samples. The optimal competition strategy was introduced at the beginning of the MCMC algorithm iteration， replacing the random difference by the directional difference， so that the samples could be moved to the target direction quickly to accelerate the computational efficiency. Based on the sampling distribution theorem， a t-distribution determination index was constructed using samples within a period of time to automatically determine whether the multi-chain MCMC converged and automatically terminated the algorithm after the sample size meets the statistical requirements， so as to reduce the computational workload of the smooth period. The numerical examples and the results of the real bridge correction show that the proposed determination method can improve the computational efficiency of the multi-chain MCMC algorithm by 30% with the same calculation accuracy， and the entire iteration process can be accelerated by about 50% considering the preset step size， which provides a method to support the application of Bayesian-based finite element model correction in large civil engineering.