In our previous papers, we gave formulas of the fine-structure constant and their corresponding applications along with a model for the masses of elementary particles. And in recent papers, we redefined Hartree atomic units to Hartree-Chen atomic units and gave formulas which determined the precise value of the Higgs boson mass. In this paper, we apply our mass model of elementary particles and Hartree-Chen atomic units to determine the exact values of the masses of the W and Z bosons. Based on our hypothetical formulas, the masses of the W and Z bosons in Hartree-Chen atomic units should be 157415.999881172 and 178449.921171171 respectively, and the exact values of the masses of W and Z bosons should be 80439.410424(24) MeV and 91187.722114(27) MeV respectively. Compared to the latest and most accurate values of 80433.5(9.4) MeV and 91187.6(2.1) MeV which were measured by the Detector Collider at Fermilab (CDF) collaboration and Large Electron-Positron Collider (LEP) respectively, our calculated values are almost absolutely precise if they are correct.