This article develops an approximate Bayesian procedure to identify the orders of vector moving average processes with seasonality. The proposed is based on approximating the likelihood function by a matrix normal – Wishart on the parameter space. Combining the approximate likelihood function with normal-Wishart or Jeffrey's' vague prior and using an indirect Bayesian technique to estimate initial values for the orders, the joint posterior mass function of the orders is developed in a convenient from. Then one may examine the posterior probabilities over the grid of the orders and select the orders at which the posterior mass function attains its maximum to be identified orders. Five simulation studies, with three different prior distributions for the order, are conducted to demonstrate the performance of the proposed procedure and check its adequacy and applicability in solving the identification problem. The numerical results support using the proposed procedure to identify the orders of vector moving average processes with seasonality.