Tensile mechanical properties tests of PP-TD20, PP + EPDM-TD20, and PP-LGF20 were conducted under quasi-static and intermediate strain rates to study the dynamic mechanical properties of polypropylene (PP) composite materials. The experimental results show that the mix of TD20 and LGF20 increases the ultimate strength of PP matrix by about 1 and 3.2 times, respectively. Ethylene propylene diene monomer (EPDM) can significantly enhance ductility. PP-TD20 and PP + EPDM-TD20 still behave ductile characteristic, while PP-LGF20 changes into a brittle material. All three materials exhibit significant strain rate sensitivity in both elastic and plastic stages. The stiffness, flow stress, yield strength, and ultimate strength increase with the rising of strain rate. The dynamic constitutive relationships of several materials were constructed by using the modified ZWT (Zhu-Wang-Tang) model and the modified J-C (Johnson-Cook) model, and the model parameters were identified. The fitting curves were basically consistent with the experimental results, indicating that these two models can accurately reflect the dynamic mechanical behavior. The modified ZWT model was extended to obtain the constitutive equation under the three-dimensional stress state, and the VUMAT subroutine was written. The load-displacement curve obtained by the numerical simulation was in good agreement with the test results, further indicating the validity of the constitutive relationship.