The paper proposes a new generalized projection type method for smooth nonlinear constrained optimization problems. The problem is transformed into one which includes inequality constraints only and which in case that the original problem involves equality constraints contains a penalty term in the objective function, where both problems are equivalent when the penalty parameter is sufficiently large. Features of the new algorithm are that the starting point can be arbitrary, that the objective function of the transformed problem is used directly as a merit function, that the penalty parameter needs to be adjusted only finitely often, and that the search direction can be computed by an explicit formula of generalized projection. Also a new line search procedure is employed. It is verified that the algorithm globally converges to KKT points of the original problem if a generalized linear independence constraint qualification is satisfied and if the sequence of points generated by the algorithm is bounded. Moreover, it is shown under a mild additional assumption that the total sequence of iteration points is convergent and that these points become feasible with respect to the constraints of the transformed problem after finitely many iterations. The performance of the new algorithm is investigated by various numerical tests.