This paper proposes a skewed multivariate probit model for analyzing a correlated binary response data with covariates. The proposed model is formulated by introducing an asymmetric link based upon a skewed multivariate normal distribution. The model connected to the asymmetric multivariate link, allows for flexible modeling of the correlation structure among binary responses and straightforward interpretation of the parameters. However, complex likelihood function of the model prevents us from fitting and analyzing the model analytically. Simulation-based Bayesian inference methodologies are provided to overcome the problem. We examine the suggested methods through two data sets in order to demonstrate their performances.