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A new type of topological state in strongly correlated condensed matter systems, the heavy Weyl fermion state, has been found in a heavy fermion material, CeRu_{4}Sn_{6}, which has no inversion symmetry. Two different types of Weyl points, types I and II, can be found in the quasiparticle band structure obtained by the LDA+Gutzwiller calculations, which can treat the strong correlation effects among the f electrons from cerium atoms. The surface calculations indicate that the topologically protected Fermi arc states exist on the (010) but not on the (001) surface.