This paper Generators is concerned with a class of discrete-time nonhomogeneous Markov jump systems with multiplicative noises and time-varying transition probability matrices which are valued on a convex polytope.The stochastic stability and finite-time stability are considered.Some stability criteria including infinite matrix inequalities are obtained by parameter-dependent Lyapunov function.Furthermore, infinite matrix inequalities are converted into finite linear matrix inequalities (LMIs) via a set shoe of slack matrices.Finally, two numerical examples are given to demonstrate the validity of the proposed theoretical methods.