In this work, we predict a novel band structure for Carbon-Lithium(C4Li) compound using the first-principles method. We show that it exhibits two Dirac points near the Fermi level; one located at W point originating from the nonsymmophic symmetry of the compound, and the other one behaves like a type-II Dirac cone with higher anisotropy along the {Gamma} to X line. The obtained Fermi surface sheets of the hole-pocket and the electron-pocket near the type-II Dirac cone are separated from each other, and they would touch each other when the Fermi level is doped to cross the type-II Dirac cone. The evolution of Fermi surface with doping is also discussed. The bands crossing from T to W make a line-node at the intersection of kx={pi} and ky={pi} mirror planes. The C4Li is a novel material with both nonsymmorphic protected Dirac cone and type-II Dirac cone near the Fermi level which may exhibit exceptional topological property for electronic applications.
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