An n-body potential is developed and satisfactorily applied to hcp metals, Co, Hf, Mg, Re, Ti, and Zr, in the form of long-range empirical potential. The potential can well reproduce the lattice constants, c/a ratios, cohesive energies, and the bulk modulus for their stable structures (hcp) and metastable structures (bcc or fcc). Meanwhile, the potential can correctly predict the order of structural stability and distinguish the energy differences between their stable hcp structure and other structures. The energies and forces derived by the potential can smoothly go to zero at cutoff radius, thus completely avoiding the unphysical behaviors in the simulations. The developed potential is applied to study the vacancy, surface fault, stacking fault and self-interstitial atom in the hcp metals. The calculated formation energies of vacancy and divacancy and activation energies of self-diffusion by vacancies are in good agreement with the values in experiments and in other works. The calculated surface energies and stacking fault energies are also consistent with the experimental data and those obtained in other theoretical works. The calculated formation energies generally agree with the results in other works, although the stable configurations of self-interstitial atoms predicted in this work somewhat contrast with those predicted by other methods. The proposed potential is shown to be relevant for describing the interaction of bcc, fcc and hcp metal systems, bringing great convenience for researchers in constructing potentials for metal systems constituted by any combination of bcc, fcc and hcp metals.