This paper presents a Bayesian approach to finding the Bayes estimator of parameters for ARMA model forecasting under normal-gamma prior assumption with a quadratic loss function in mathematical expression. Obtaining the conditional posterior predictive density is based on the normal-gamma prior and the conditional predictive density, whereas its marginal conditional posterior predictive density is obtained using the conditional posterior predictive density. Furthermore, the Bayes estimator of parameters is derived from the marginal conditional posterior predictive density.