Recent years have witnessed intense activity concerning the study of nuclei with equal numbers of neutrons and protons (N = Z). Exotic properties have been exhibited in the N = Z nuclei, especially in those with atomic masses around 80. In the present paper, the projected shell model (PSM) together with a relativistic Hartree-Bogoliubov (RHB) theory is used to study the nuclear structure near the N = Z line in the mass A≈ 80 region. For three Zr isotopes ~(80,82,84)Zr, the projected potential energy surfaces and ground state bands are calculated. It is shown that shape coexistence occurs in all of these nuclei. Moreover, we find that the residual neutron-proton interaction strongly affects the ground state band of ~(80)Zr; however, it slightly modifies those of ~(82)Zr and ~(84)Zr.