In this paper, we discuss the parallel solution of variational inequalities on a general closed convex setK. First a sufficient and necessary condition will be given for the convergence of the parallel algorithm proposed in [10] which is suitable only in the case ofKbeing a closed convex cone. Second we present algorithms which work for the parallel computations on general closed convex sets. After that the parallel solution of linear complementary systems related to variational inequalities will be investigated. Finally numerical experiments will be reported to show the convergence of the algorithms.