Abstract: In the problem of stochastic control, the steady-state variances and closed-loop poles of the control systems, which respectively represent the steady-state and transient -state behaviour, are two important performance requirements. The problem addressed in this paper is to design the dynamic output feedback controller such that the steady-state variance is not greater than the desired upper bound and the closed-loop poles lie within the prescribed circular region. The existence conditions and the analytical expression of the expected controllers are obtained. A numerical example is provided to show the effectiveness of the method.