An n-body potential is constructed for the Ni-Nb-Ta ternary metal system in the newly proposed form of long-range empirical potential. The constructed Ni-Nb-Ta potential can well reproduce the lattice constants, cohesive energies, and elastic modulus of the metals and some compounds as well as the equations of state of the system. Applying the constructed Ni-Nb-Ta potential, molecular dynamics simulations and Voronoi tessellations are carried out to study the issues related to the Ni-Nb-Ta metallic glasses. It is found that increasing the Ni content can obviously improve the glass-forming ability of the binary Nb-Ta system, which features a isomorphous phase diagram unfavoring for forming glass, indicating that the Ni solute plays a decisive role in forming the Nb-based or Ta-based Ni-Nb-Ta metallic glasses. Concerning the atomic structure, the Voronoi cell volume and coordination number (CN) of Ta are generally larger than those of Ni in the binary Ni-Ta metallic glasses. With increasing the Ni concentration, the fraction of icosidihedron (CN = 13) increases, while the fractions of icosihexahedron (CN = 15) and icosioctahedron (CN = 16) decrease. Meanwhile, with increasing the Ni concentration, the dominating coordination numbers of Ta atoms increase. Interestingly, similar feature in the atomic structure with variation of Ni concentration is also observed in the Ni-Nb metallic glasses. For the ternary Ni-Nb-Ta alloys, it is observed from the CN distributions that the structure of the metallic glasses is mostly affected by the Ni concentration.