Abstract: The consistency of constraint indices of state variance and circular pole is studied for a class of stochastic systems with state feedback control. Two necessary and sufficient conditions are given, in terms of linear matrix inequalities (LMIs), for the existence of state feedback control with circular pole constraints. Satisfactory control design methods are provided for state feedback control with constraints of circular pole and consistent state-variance. By finding the maximum and minimum of matrix trace subject to LMIs, a good range is presented for all steady state-variance which is consistent with the given regional pole. Finally, an example illustrates that obtained results in this paper are of simplicity and validity.