Abstract: The problem of state estimation with the steady-state estimation error variance constraints and the circular pole constraints is proposed and studied in this paper. The purpose of this problem is to design the filter gain such that the steady-state value of estimation error variance for each state is less than or equal to the prespecified value, and the poles of the filter matrix lie within the prespecified circular region, simultaneously. Therefore the filtering process will possess good behavior. It is shown that the solution of the addressed problem can be determined by a modified Riccati equation. The conditions for the existence and the explicit expression of the desired filter gains are given, Finally, a numerical example is provided to demonstrate the directness and simplicity of the present design method.