The application of Bayesian methods to infrastructure deterioration prediction models based upon monitoring data collected through inspection activities has been increased in the past ten years. Usually, the Bayesian techniques can be implemented to estimate the model unknown parameters associated with inspection activities as well as the pre-defined prediction models. However, for many models, due to the complexity of the data structure and limited prior knowledge of target distributions, conventional sampling algorithms, such as MCMC algorithms using the Metropolis–Hastings sampling, can be inefficient and impractical which leads to struggling to obtain approximate solutions for the posterior distribution of the model unknown parameters. In this paper, a Differential Evaluation Markov Chain Monte Carlo (DE-MCMC) method is introduced to enhance the estimation of Markov transition probability of the multi-stage exponential hazard Markov chain model. An empirical example is presented to demonstrate the applicability of the model and its DE-MCMC estimation algorithm by using time-series data of railway track geometry condition monitoring data from Japan. The case study results indicate the effectiveness of the proposed DE-MCMC algorithm in improving the estimation of infrastructure deterioration prediction model.