This paper is concerned with the problem of passivity-based asynchronous sliding mode control for a class of uncertain singular Markovian jump systems with time delay and nonlinear perturbations. The asynchronous control strategy is employed due to the nonsynchronization between the controller and the system modes. Considering the singularity of the system, a novel integral-type sliding surface is constructed, and then the asynchronous sliding controller is synthesized to ensure that the sliding mode dynamics satisfy the reaching condition. Sufficient conditions are presented such that the corresponding sliding mode dynamics are admissible and robustly passive. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed technique.