This paper is interested in the   Efficiency of the approximate Bayesian Prediction of ARMA Models. Three different approximate one step-ahead predictive densities using three different   approximate are considered. These  approximations are proposed by Newbold (1973), Zellner and Reynolds (1978) and Broemeling and Shaarawy (1988). Simulation is employed to study and compare the performance of the three  approximate one-ahead predictive densities using some ARMA models. Simulation results show that, there is no remarkable difference between the three   approximate one-ahead predictive densities in their efficiency. Moreover, their first two moment converge to those of the exact one step-ahead predictive density.