Abstract: Kundu and Gupta proposed to use the importance sampling method to compute the Bayesian estimation of the unknown parameters of the Marshall-Olkin bivariate Weibull distribution. However, we find that the performance of the importance sampling method becomes worse as the sample size gets larger. In this paper, we introduce latent variables to simplify the likelihood function, and use MCMC algorithm to estimate the unknown parameters. Numerical simulations are carried out to assess the performance of the proposed method by comparing with the maximum likelihood estimation, and we find that the Bayesian estimates perform better even for the case of small sample size. A real data is also analyzed for illustrative purpose.