A new type of topological state in strongly corrected condensed matter systems, heavy Weyl fermion state, has been found in a heavy fermion material CeRu4Sn6, which has no inversion symmetry . Both two different types of Weyl points, type I and II, can be found in the quasi-particle band structure obtained by the LDA+Guztwiller 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) surfaces.Recently different types of topological semimetals [1] have been proposed and observed in condensed matter systems, i.e. the Weyl semimetal(WSM) phase in transition metal compounds with the magnetic order, [2, 3] WSM phase in non-central symmetric crystals, [4-9] Dirac semimetal (DSM) phase in intermetallic compounds [10][11][12][13][14][15] and nodal line semimetal phase in anti-perovskite compounds. [16,17] In all the abovementioned material systems, the electron-electron correlation effect is weak, and the band structure, as well as the existence of Weyl nodes, can be obtained quite accurately by density functional theory. On the other hand, the topological non-trivial electronic structure can be found in strongly correlated material systems as well, for instance, the topological Kondo insulator phase in SmB 6 [18-20] can be viewed as the strongly correlated Z 2 topological insulator, which has attracted lots of research interests in recent years. [21][22][23][24][25] In SmB 6 , the correlation effects generated by the strong Coulomb repulsive interaction among f -electrons suppress the bandwidth dramatically but leave the topological features of the electronic structure unchanged [20,24,26,27].In the present letter, we propose that CeRu 4 Sn 6 , [28-32] a typical heavy fermion material, contains Weyl points in its quasiparticle band structure near the Fermi level and thus belongs to a new class of strongly correlated topological phase, heavy Weyl fermion state. Comparing to other WSMs found in non-interacting systems, the WSM phase in heavy fermion system has more fruitful physical properties due to the following reasons. Firstly, unlike the non-interacting systems, the heavy quasiparticle bands are fully developed only at the low temperature. Therefore, how the physics related to the topological electronic structure evolves as the decrement of temperature will become an crucial problem for the heavy Weyl fermion phase, which may lead to new unique phenomena in these systems. Secondly, in heavy fermion systems, the energy scale of the quasiparticle bands is orders smaller than the ordinary semiconductor or semimetal systems, which makes it more sensitive to various of the external field, i.e. the pressure, mag-netic field and strain, providing large tunability to the distribution of the Weyl nodes. kx ky kz Γ Z N Σ X P (001) Surface (010) Surface (a) (b) FIG. 1. (Color online) Crystal structure and Brillouin zone (BZ). (a) The crystal symmetry of CeRu4Sn6...