In this paper a unified linear matrix inequality (LMI) approach to the design of reduced-order controllers for both continuous and discrete-time singular H-infinity control problems is proposed. For the singular case where the direct feedthrough from the input to the error and from the exogenous signal to the output are no longer of full rank, it is proved for both continuous and discrete time cases that reduced-order controllers with orders less than the generalized plant order exist if the singular H-infinity control problems are solvable. An algorithm for constructing the controllers is given. In comparison with previous results, no assumption about zeros on finite j omega-axis or zeros in unit circle is needed in this paper.