Polyethylene (PE) is an important kind of plastic, which plays a significant role as the shell material of the fuel capsule, light weight structural element subjected to intense mechanical impact and explosion load. And it is well accepted that semi-empirical three-term equation of state (EOS) is one of the most widely used EOSs in practical work. Therefore, studies of semi-empirical three-term EOS of PE are significant for accurately predicting and analyzing the physical processes and experimental results under high pressure compression. A semi-empirical three-term complete EOS of PE based on the model of Helmholtz free energy is established in this work. According to the EOS model, the Helmholtz free energy is composed of cold energy, thermal contribution of atoms and thermal excitation of electrons. The cold energy is calculated by using the Mie potential. The optical frequency branch of atomic vibration and the thermal contribution of electrons are neglected in the calculation at temperatures below 104 K. The parameters of Helmholtz free energy are calculated by using the shock Hugoniot data and thermal parameters at ambient state. And then, the application pressure range and reliability of the semi-empirical three-term EOS of PE are evaluated. Shock Hugoniot, shock wave temperature and Grneisen coefficient of PE are deduced from the EOS. The results show that shock Hugoniot and shock wave temperature are consistent well with the experimental data and the first-principle calculation in a pressure range of 150 GPa. Because the specific volume of PE does not change obviously in the melting and chain dissociation process, the assumption of linear Hugoniot relation of PE is valid for calculating the cold energy parameters. The calculation results deviate from the experimental results at about 150 GPa while the compression lasts up to the chemical bond dissociation pressure of PE. In addition, the value of buck modulus and its derivative with respect to pressure at zero pressure and temperature depend strongly on Hugoniot parameters. Therefore, the parameter of Helmholtz free energy in this work is only valid for compression. In conclusion, the Helmholtz free energy model and parameters can well reproduce the experimental data and reasonably describe the thermodynamic state of PE at its dissociation pressure. Moreover, it should be pointed out that a more refined model of phase transition and thermal contribution of atoms and electrons should be considered when extrapolated to higher pressure.