The finite-time stability for a class of discrete-time stochastic Markov jump systems with multiplicative noises is studied.The transition probability matrix is not a constant matrix but a interval matrix.Under the assumption of the compactness of the interval matrix, it is represented as a convex combination of some random matrices.Firstly, the sufficient and necessary condition of finite-time stability is given.Then, a sufficient condition for the finite-time stability of the system is obtained and the finite-time stabilization controller with state feedback is designed by using the Lyapunov method and linear matrix inequality technique.Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.