This paper investigates the finite-time asynchronous control issue for singular fuzzy Markov jump systems (SFMJSs) with mode-dependent derivative-term coefficient through the sliding mode control (SMC) approach. Firstly, a new adaptive event-triggered scheme (ETS), which satisfies the system conditions by changing the threshold, is adopted to further reduce the communication consumption. Meanwhile, a mode-dependent fuzzy sliding surface (SS) function on account of hidden Markov model is designed. Based on a state observer, an asynchronous SMC law is proposed in accordance with the adaptive ETS to ensure that SFMJSs are finite-time boundedness (FTB). Finally, two examples are provided to certify the availability and practicability of the presented results.