In this paper, the problem of circular pole and variance-constrained state estimator design is studied for perturbed linear continuous-time systems. The system under consideration is subject to unstructured time-invariant norm-bounded parameter perturbations in both the state and measurement matrices. The problem we address is the design of a state estimator such that, for all admissible time-invariant perturbations, the poles of the steady-state filtering matrix are assigned inside a prespecified circular region, and the variance of the estimation error of each state is not more that the individual prespecified value, simultaneously. An algebraic Riccati-like matrix inequality approach is proposed to solve the above problem. Specifically, the existence conditions and an explicit expression for the desired estimators are obtained. Furthermore, an illustrative example is presented to demonstrate the effectiveness of the proposed design procedure.