We present CoTe2 as a new type-II Dirac semimetal supporting Lorentz symmetry violating Dirac fermions in the vicinity of the Fermi energy. By combining first principle ab-initio calculations with experimental angle-resolved photo-emission spectroscopy results, we show the CoTe2 hosts a pair of type-II Dirac fermions around 90 meV above the Fermi energy. In addition to the bulk Dirac fermions, we find several topological band inversions in bulk CoTe2, which gives rise to a ladder of spin-polarized surface states over a wide range of energies. In contrast to the surface states which typically display Rashba-type in-plane spin splitting, we find that CoTe2 hosts novel out-of-plane spin polarization as well. Our work establishes CoTe2 as a potential candidate for the exploration of Dirac fermiology and applications in spintronic devices, infrared plasmonics, and ultrafast optoelectronics.