Abstract: In this paper, we study optimal policies for a class of continuous-time Markov control processes (CTMCPs) with infinite horizon average-cost criteria. Using the basic properties of infinitesimal generators and performance potentials, we give directly the optimality equation and establish the existence of solutions to this equation for the average-cost model on a compact action set. A fast value iteration algorithm, which leads to an ε-optimal stationary policy, is proposed and the convergence of this algorithm is studied. Finally, we provide one numerical example to show applications of the proposed method.