This paper addresses the dissipative asynchronous filtering problem for a class of Takagi-Sugeno fuzzy Markov jump systems in the continuous-time domain. The hidden Markov model is applied to describe the asynchronous situation between the designed filter and the original system. Based on the stochastic Lyapunov function, a sufficient condition is developed to guarantee the stochastic stability of the filtering error systems with a given dissipative performance. Two different methods for the existence of desired filter are established. Due to the Finsler's lemma, the second approach has fewer variables to decide and brings less conservatism than the first one. Finally, an example is provided to demonstrate the correctness and advantage of the proposed approaches.