In this paper, we develop a Bayesian hierarchical model and associated computation strategy for simultaneously conducting parameter estimation and variable selection in binary quantile regression. We specify customary asymmetric Laplace distribution on the error term and assign quantile-dependent priors on the regression coefficients and a binary vector to identify the model configuration. Thanks to the normal-exponential mixture representation of the asymmetric Laplace distribution, we proceed to develop a novel three-stage computational scheme starting with an expectation–maximization algorithm and then the Gibbs sampler followed by an importance re-weighting step to draw nearly independent Markov chain Monte Carlo samples from the full posterior distributions of the unknown parameters. Simulation studies are conducted to compare the performance of the proposed Bayesian method with that of several existing ones in the literature. Finally, two real-data applications are provided for illustrative purposes.