In this paper we use the Gibbs sampling algorithm to develop a Bayesian inference for multiplicative double seasonal moving average (DSMA) models. Assuming the model errors are normally distributed and using natural conjugate priors, we show that the conditional posterior distribution of the model parameters and variance are multivariate normal and inverse gamma respectively, and then we apply the Gibbs sampling to approximate empirically the marginal posterior distributions. The proposed Bayesian methodology is evaluated using simulation study.