The problem of asynchronous dissipative control is investigated for Takagi-Sugeno fuzzy systems with Markov jump in this paper. Hidden Markov model is introduced to represent the nonsynchronization between the designed controller and the original system. By the fuzzy-basis-dependent and mode-dependent Lyapunov function, a sufficient condition is achieved such that the resulting closed-loop system is stochastically stable with a strictly (<inline-formula> <tex-math notation="LaTeX"> {\mathcal {Q}} </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX"> {\mathcal {S}} </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX"> {\mathcal {R}} </tex-math></inline-formula>)-<inline-formula> <tex-math notation="LaTeX"> {\alpha } </tex-math></inline-formula>-dissipative performance. The controller parameter is derived by applying MATLAB to solve a set of linear matrix inequalities. Finally, we present two examples to confirm the validity and correctness of our developed approach.