This paper is concerned with the problem of designing a robust L_2 L\infty filter for a class of uncertain systems subject to error variance and circular pole constraints. Specifically, we aim to design a filter such that the L_ L\infty norm of the filtering error-transfer function is not less than a given upper bound, while the poles of the filtering matrix are assigned within a prespecified circular region, and the steady-state error variance for state is not more than the prespecified value. The filter design problem is formulated as an auxiliary matrix assignment problem. Both the existence condition and the explicit expression of the desired filters are then derived by using an LMI approach. The proposed design algorithm is illustrated by a numerical example.