A molecular network constitutive model is proposed in this study. Based on the concept of molecular network decomposition, the molecular network was decomposed into a James–Guth 3-chain network model and an Arruda–Boyce 8-chain network model. Considering that the single molecular chain of rubber is constrained by the surrounding molecular networks, the 3-chain model and the 8-chain model were consequently modified using the tube theory. The proposed model contains four material parameters that were determined by fitting the uniaxial tensile test data from rubber-like materials, and the values of these parameters were utilized to determine the pure shear and the biaxial extension. The proposed model agrees well with the experimental data and can predict the test results of experiments performed under the conditions of pure shear and equi-biaxial deformation with acceptable accuracy.