This paper solves the H-2 output feedback control problem for continuous-time descriptor systems. An existence condition of the H-2 optimal controller is derived based on the standard model matching technique, and a characterization of the optimal controller is given in terms of the solutions of two generalized algebraic Riccati equations. It turns out that the optimal controller has an observer-based structure well-known in the state-space case, so that the results in this paper are natural extensions of the state-space results to the descriptor systems. A numerical example is also included to show the applicability of the proposed results.