In this study, electroencephalography (EEG) inverse problem is formulated using Bayesian inference. The posterior probability distribution of current sources is sampled by Markov Chain Monte Carlo (MCMC) methods. Sampling algorithm is designed by combining Reversible Jump (RJ) which permits trans-dimensional iterations and Simulated Annealing (SA), a heuristic to escape from local optima. Two different approaches to EEG inverse problem, Equivalent Current Dipole (ECD) and Distributed Linear Imaging (DLI) are combined in terms of probability. EEG inverse problem is solved with this probabilistic approach using simulated data on a realistic head model. Localization errors are computed. Comparing to Multiple Signal Classification algorithm (MUSIC) and Low-Resolution Electromagnetic Tomography (LORETA), using MCMC methods with a Bayesian approach is useful for solving the EEG inverse problem.