Distinct to type-I Weyl semimetals (WSMs) that host quasiparticles described by the Weyl equation, the energy dispersion of quasiparticles in type-II WSMs violates Lorentz invariance and the Weyl cones in the momentum space are tilted. Since it was proposed that type-II Weyl fermions could emerge from (W,Mo)Te_{2} and (W,Mo)P_{2} families of materials, a large number of experiments have been dedicated to unveiling the possible manifestation of type-II WSMs, e.g., surface-state Fermi arcs. However, the interpretations of the experimental results are very controversial. Here, using angle-resolved photoemission spectroscopy supported by the first-principles calculations, we probe the tilted Weyl cone bands in the bulk electronic structure of WP_{2} directly, which are at the origin of Fermi arcs at the surfaces and transport properties related to the chiral anomaly in type-II WSMs. Our results ascertain that, due to the spin-orbit coupling, the Weyl nodes originate from the splitting of fourfold degenerate band-crossing points with Chern numbers C=±2 induced by the crystal symmetries of WP_{2}, which is unique among all the discovered WSMs. Our finding also provides a guiding line to observe the chiral anomaly that could manifest in novel transport properties.