This note investigates the asynchronous control issue for continuous-time Markov jump nonlinear systems using output-based sliding mode approach. A hidden Markov model of interest is used as the mapping mechanism of the asynchronous phenomenon, which further contributes to the asynchronous sliding mode surfacce. In this scenario, sufficient conditions are derived ensuring the mean-square-stability of the sliding motion dynamic and its H∞ noise attenuation performance. Then the reachability of the sliding surface is guaranteed by a well defined reaching control law. Finally a numerical example is presented to discuss the significance of the proposed asynchronous issue and verify the effectiveness of the designed control approach.