<p>In this paper, we consider a distributionally robust optimization problem with probabilistic envelope constraints that provides different probabilistic guarantees at each level of constraint violation. Indeed, it is a generalization of chance constraints. We require the robust chance constraints hold with respect to all probability distributions over 1-Wasserstein ball centered at a discrete empirical distribution. Then we derive a non-convex upper bound problem and employ a sequential convex approximation algorithm to solve it. Furthermore, we develop a lower bound approximation which is equivalent to a mixed-integer linear programming formulation. Numerical results on a portfolio optimization problem illustrate the convergency and effectiveness of the proposed two approximation methods.</p>