Using the cone theory and non-symmetric iteration method, the existence and uniqueness of the solutions of a class of non-linear operator equations A (x,x) + uO = Bx without continuity and compactness conditions are studied. And the error estimates that the iterative sequences converge to solutions are also given. The results presented here are of the improvement and generalization of some corresponding results. Non-symmetric iteration method is another efficient method of solving the integral equation and the problem that can't be dealt with by using the symmetric iteration method in the semi-ordered space.