This paper considers the problem of $H_{infty}$ dynamic output feedback (DOF) control for a class of stochastic systems with time-varying delay and $L_{infty}$ disturbance. A new delay-dependent sufficient condition for the existence of the DOF controller is derived and the controller design method is given in the form of bilinear matrix inequalities (BMIs). Moreover, a variable step size path-following algorithm is proposed to solve the BMI problem. Numerical examples are given to illustrate the effectiveness of the proposed methods.