Bayesian analysis provides a framework for the inverse uncertainty quantification (UQ) of combustion kinetic models. As the workhorse of the Bayesian approach, the Markov chain Monte Carlo (MCMC) methods, however, incur a substantial computational cost. In this work, a surrogate model is employed to improve the traditional MCMC algorithm. Specifically, the test errors of three typical surrogate models are compared, namely Polynomial Chaos Expansion (PCE), High Dimensional Model Representation (HDMR) and Artificial Neural Network (ANN); and ANN is shown to be a relatively more efficient surrogate model for the approximation of combustion reaction systems under extensive conditions. An inverse UQ method, which is the combination of the ANN and traditional MCMC method, and as such termed ANN-MCMC, is adopted. The calculation is performed on the methanol oxidation system and a series of ignition delay data are employed to optimize the rate coefficients of the kinetic model. The estimated posterior distributions of the rate coefficients and the model predictions using the ANN-MCMC are compared with the traditional MCMC methods, with the results showing that the ANN-MCMC can significantly reduce the computational cost needed for the MCMC algorithm, especially on the estimation of the posterior distributions of the input parameters. The rejection rate of the samples in a Markov chain is very high, especially for the calculation of the posterior distribution of less sensitive parameters, thus a large number of samples are needed to reach a desired accuracy for traditional MCMC process. While no samples are rejected when training the ANN surrogate model. Therefore, fewer original samples are needed to get a converged ANN surrogate, which can then generate a large number of low-cost ANN samples for a better accuracy of the MCMC process. The errors for the estimated posterior distributions using ANN-MCMC depend on the accuracy of converged ANN surrogates and more accurate results are obtained with improved settings of ANN. The ANN-MCMC is especially suitable to the computational systems when the computational ability is limited. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.