In order to simulate the elastic-plastic behavior of concrete better, an effective curve fitting method is employed to find the constitutive function based on Legendre orthogonal polynomial and least square method. And a new numerical analysis program using arch-length method to deal with nonlinear problem is designed. The most important consequence is that not only the fitting function, but also its derivative function and its definite integral are recursive. The fitting curve given by new method is applied in numerical analyzing. Cube model is examined under uniaxial compressing with completely restricted boundary conditions. The results show convex deformation and the damage on oblique section clearly. Compared with those piecewise fitting functions, the Legendre orthogonal polynomial fitting function obtained can be introduced into the nonlinear harden-soften character of concrete constitute law more convenient because of its uniform function form and continuous derived feature. And the fitting idea by orthogonal base function will provide a widely road for studying the constitute law of concrete material.