In this work, we consider an evolution model formulated by a parabolic differential inclusion and a parabolic variational inequality. We prove the solvability of our problem and show that the solution set generates a m-semiflow. In addition, the existence of a global attractor for the m-semiflow is proved by using the technique of measure of noncompactness. An example is given to illustrate our theoretical results for an evolution system arising from a Stefan problem.