For a descriptor system with time-varying structured uncertainty, this paper considers the robust H-2 control problem of finding a controller satisfying the prescribed H-2 performance level against all possible uncertainty under the constraint of robust stability. A sufficient condition for the robust H-2 performance is derived in terms of a linear matrix inequality (LMI). Based on this LMI condition, we develop a design method of a descriptor variable feedback controller achieving the robust performance. The present design method can solve the robust H-2 control problem for a wider class of plants than the state-space approach. A numerical example is also included to show the applicability of the present method.