In the tension and compression tests under quasi-static loading, almost all polymer bonded explosives (PBXs) reflect obviously nonlinear constitutive behavior, now commonly used constitutive model in the description of the nonlinear adaptability is not ideal. Aimming at the nonlinearity and asymmetry of stress-strain curves for five typical PBXs (PBX-X, PBX-9502, LX-17, PBX-9501, and EDC-37), a quasi-static constitutive model with four parameters that considers both tension and compression was deduced based on Boltzmann function. Based on the discussion of the physical meaning of undetermined parameters for the model, on account of determined method of undetermined parameters proposed in this paper, the stress-strain curves for five kinds of typpical PBXs were fitted by the constitutive model. Results show that the constitutive model can well describe the constitutive behavior at different temperatures and strain rates for typpical PBXs. The constitutive model of tension and compression based on the Boltzmann function is expected to be widely used as a universal quasi-static constitutive model for different PBX materials.