<p>In this paper, the problem of asynchronous sliding mode control for a class of Markov jump systems with time-varying delay is investigated by using an event-triggered protocol. This phenomenon of asynchrony between the sub-system modes and the sub-controller modes will be considered in this work. The stabilization of sliding mode dynamic is guaranteed by proposing a Lyapunov-Krasovskii function with the help of advanced inequality theories. To achieve such a goal, a dynamic event-triggered protocol is developed to help the controller make a good trade-off between control performance and transmission efficiency. Furthermore, a modified asynchronous sliding mode controller is developed to alleviate the chattering problem induced by the sign function. With the designed controller, the system trajectory can be driven onto the sliding surface in a finite time and remains there thereafter. Additionally, the Zeno phenomenon is proved to be impossible. Finally, two practical examples are presented to demonstrate the validity of the theoretical results.</p>