Abstract: This paper deals with the average cost optimization problem for a class of discrete time Markov control processes. Under quite general assumptions, the optimality equation is directly established and the existence theorem of optimal solution is proved for infinite time average cost model in a compact action set by using basic properties of the Markov performance potentials. The iterate algorithm for solving optimal stationary control strategy is suggested and the convergence problem of this algorithm is discussed. Finally, a numerical example is analyzed to illustrate the application of the proposed algorithm.