This paper extends the method of M. A. Noor
and A. Bnouhachem
[J. Comput. Appl. Math. 197, No. 2, 395–405 (2006; Zbl 1120.90062
)], and propose a method for solving nonlinear complementarity problems (NCP), where the underlying function F is pseudomonotone and continuous by performing an additional projection step at each iteration and another optimal step length is employed to reach substantial progress in each iteration. The authors prove the global convergence of the proposed method under some suitable conditions. Some preliminary computational results are given to illustrate the efficiency of the new proposed method. The numerical results show that the new method is attractive in practice. It also demonstrates computationally that the new method is more effective than the method presented in Noor and Bnouhachem [loc. cit.] in the sense that the new method needs fewer iterations and less computational time.