This paper is to study the discrete-time stochastic H-2/H-infinity control with state and external disturbance dependent noise. A necessary and sufficient condition for the existence of H-2/H-infinity control is presented, which transforms the H-2/H-infinity controller design into solving four coupled matrix-valued equations. Moreover, a recursive algorithm for solving the four coupled matrix-valued equations is also given. (C) 2006 Elsevier Ltd. All rights reserved.