This paper deals with the infinite horizon optimal control problem for deterministic Boolean control networks (BCNs) with average cost. Based on the semi-tensor product of matrices and Jordan decomposition technique, a nested optimality equation for the average infinite horizon problem of BCNs is presented. By resorting to Laurent series expression, a novel policy iteration algorithm, which can find the optimal state feedback controller in finite iteration steps, is proposed. Finally, as a practical application, the optimal intervention problem of Ara operon in E. coil is addressed. (C) 2018 Elsevier Ltd. All rights reserved.