A numerical method has been proposed for solving strongly nonlinear simultaneous equations with two variables by improving the Wegstein method for one variable. The features of the proposed method are i) to use only an initial value, ii) to provide stability of the solution with simplicity of algorithm, and iii) to reduce the C. P. U. time required. The superiority of this method is demonstrated by two sample calculations, bubble point at chemical equilibrium and a quenching.