This paper is a sequel to the analysis of finite-step approximations in solving controlled Markov set-chains for infinite horizon discounted reward by the author. For average-reward-controlled Markov set-chains with finite state and action spaces, we develop a value-iteration-type algorithm and analyze an error bound relative to the optimal average reward that satisfies an optimality equation from the successive approximation under an ergodicity condition. We further analyze an error bound of the rolling horizon control policy defined from a finite-step approximate value by applying the value-iteration-type algorithm.