The finite-time control of discrete-time stochastic Markov jumping systems with multiplicative noise is studied. Firstly, the definitions of finite-time stability and finite-time boundedness are given. The necessary and sufficient condition of finite-time stability is obtained by successive iteration and conditional expectation. Then, the sufficient condition and the state feedback controller design of the system with disturb are realized by using the Lyapunov method and linear matrix inequality technology. Furthermore, the finite-time boundedness is considered under the incomplete information of transition probability. Finally, the effectiveness of the introduced method is verified by a numerical example.