This paper mainly studies the finite-time $H_{\infty}$ control problem of discrete-time Markov jump system based on dynamic output feedback. In view of the unmeasurable state and external disturbance in the actual system, a dynamic output feedback control strategy is proposed. At the same time, based on the finite-time $H_{\infty}$ control theory and Markov jump system theory, the stability of the closed-loop system is analyzed and the feasible sufficient conditions are obtained by using linear matrix inequality (LMI) technology.The proposed method gives a more relaxed matrix inequality decoupling scheme, which has a larger scope of application. Finally, the effectiveness of the proposed control scheme is verified by numerical examples.