In this paper, the finite horizon mixed H-2/H-infinity control problem is studied for the systems governed by Ito-type nonlinear stochastic differential equations with state, control and external disturbance-dependent noise. It is shown that the mixed H-2/H-infinity control under consideration is associated with the four cross-coupled Hamilton-Jacobi equations. A discrete approximation algorithm is presented for solving the coupled generalized differential Riccati equations arising from linear stochastic H-2/H-infinity control. A necessary condition and a sufficient condition for the existence of the finite horizon stochastic H-2/H-infinity control are derived. In particular, some previous results on deterministic and stochastic H-2/H-infinity control can be viewed as corollaries of our main theorems. (c) 2006 Elsevier Ltd. All rights reserved.