The problem of delay-dependent H∞ control is considered for singular Markovian jump systems with time delay. The aim of the problem is to design a state feedback controller, which guarantees that the resultant closed-loop system is not only regular, impulse free and stochastically stable, but also satisfies a prescribed H∞ performance level for all delays no larger than a given upper bound in terms of linear matrix inequality (LMI) approach. A strict LMI condition is developed to guarantee the existence of the desired state feedback controller. An explicit expression for the desired controller is also given. Numerical examples show the effectiveness of the proposed methods. Copyright © 2008 John Wiley & Sons, Ltd.