Based on a Lyapunov-Krasovskii functional, a new delay-dependent H infinity performance criterion is established for stochastic systems with discrete and distributed delays. It is shown that the H infinity -performance of the corresponding uncontrolled stochastic perturbed system is equivalent to the existence and uniqueness of solutions to the finite horizon stochastic H 2 / H infinity control problem. The resulting H 2 / H infinity controller is characterised by a kind of generalized forward-backward stochastic differential equations with delayed stochastic differential equations as forward equations and generalized anticipated backward stochastic differential equations as backward equations. A practical example is given to illustrate the proposed method.