Pseudomonotone variational inequalities have been investigated by many authors, a common assumption " weak sequential continuity " being imposed on pseudomonotone operators. In this paper, we propose an iterative procedure for solving pseudomonotone variational inequalities and fixed point problems of asymptotically pseudocontractive operators by using self-adaptive techniques. Under a weaker assumption than weak sequential continuity imposed on pseudomonotone operators, we prove that the suggested procedure has strong convergence.