Combined with Jones-Nelson-Morgan model applied to ceramics and graphite successfully, the nonlinear constitutive model of concrete is obtained through large number of tests in this paper. The model takes concrete as nonlinear elastic isotropic material. By using strain energy function, it makes the nonlinear mechanics behavior of concrete as the function of strain energy. According to the mechanics behavior of concrete, a simple model is obtained by increasing stress to realize the model calculation program. The model can be extended to the constitutive model analysis of concrete under biaxial stress. The theoretical model conforms to testing results well.