This paper studies the proximal point algorithm for the class of generalized 0P variational inequalities. By using the upper semicontinuity result establishing the class of weakly univalent operators, we show that the iterative sequence generated by the algorithm is bounded, approaches to the solution set of the initial problem, and each of its accumulation points is a solution to the problem, provided that the solution set is bounded. We also give an example to show the necessity of boundedness.