In this paper we consider a computer method of the formal linearization for nonlinear systems. A nonlinear system is described by a system of nonlinear ordinary differential equations. A linearization function is given as a solution of a system of linear partial differential equations. It is solved by the procedure of weighted residual based on the orthogonal polynomials with the aid of computers. The error bound and the application of the method are also considered. Numerical examples show that the accuracy of the method is improved as the order of the polynomials increases.