With the advantages of a moderate band gap, high carrier mobility and good environmental stability, two-dimensional (2D) semiconductors show promising applications in next-generation electronics. However, the accustomed metal-2D semiconductor contact may lead to a strong Fermi level pinning (FLP) effect, which severely limits the practical performance of 2D electronics. Herein, the interfacial properties of the contacts between a promising 2D semiconductor, PtSe2, and a sequence of metal electrodes are systematically investigated. The strong interfacial interactions formed in all metal-PtSe2 contacts lead to chemical bonds and a significant interfacial dipole, resulting in a vertical Schottky barrier for Ag, Au, Pd and Pt-based systems and a lateral Schottky barrier for Al, Cu, Sc and Ti-based systems, with a strong FLP effect. Remarkably, the tunneling probability for most metal-PtSe2 is significantly high and the tunneling-specific resistivity is two orders of magnitude lower than that of the state-of-the-art contacts, demonstrating the high efficiency for electron injection from metals to PtSe2. Moreover, the introduction of h-BN as a buffer layer leads to a weakened FLP effect (S = 0.50) and the transformation into p-type Schottky contact for Pt-PtSe2 contacts. These results reveal the underlying mechanism of the interfacial properties of metal-PtSe2 contacts, which is useful for designing advanced 2D semiconductor-based electronics.