This paper 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 of slack matrices. Finally, two numerical examples are given to demonstrate the validity of the proposed theoretical methods.