In this article we propose a new approach for solving nonlinear boundary value problems that often arise in similarity variable boundary layer problems defined over semi-infinite domains. The proposed method, called the spectral relaxation method (SRM), is based on simple iteration schemes formed by reduction of the order of the momentum equation followed by a rearrangement of the resulting governing nonlinear equation systems. Unlike most iterative schemes used for solving nonlinear systems of equations, the SRM does not require any evaluation of derivatives, perturbation, and linearization. Numerical experiments are presented to establish the validity of the proposed method on selected boundary layer problems of different complexities. The numerical convergence and accuracy of the results are presented. The obtained results indicate that the method is accurate, effective, and easy and can be used as a convenient method for solving a wide variety of highly nonlinear systems of similarity boundary layer equations and other classes of boundary value problems.