We have developed a new algorithm for nonlinear optimization problems with simple constraints. This algorithm is a natural extension of our unconstrained optimization algorithm described in Cheung and Ng, 1995. It has shown to be very efficient and robust and has compared favourably with some existing nonlinear optimization algorithms. Furthermore, we have deviced a workable method to avoid being entrapped into a local optimal point so that the ultimate solution obtained is most likely to be a global optimal solution.