We have studied the nature of the three-dimensional multi-band electronic structure in the twodimensional triangular lattice Ir1−xPtxTe2 (x=0.05) superconductor using angle-resolved photoemission spectroscopy (ARPES), x-ray photoemission spectroscopy (XPS) and band structure calculation. ARPES results clearly show a cylindrical (almost two-dimensional) Fermi surface around the zone center. Near the zone boundary, the cylindrical Fermi surface is truncated into several pieces in a complicated manner with strong three-dimensionality. The XPS result and the band structure calculation indicate that the strong Te 5p-Te 5p hybridization between the IrTe2 triangular lattice layers is responsible for the three-dimensionality of the Fermi surfaces and the intervening of the Fermi surfaces observed by ARPES.PACS numbers: 74.70. Xa, 74.25.Jb, 71.30.+h, 3d, 4d, and 5d transition-metal compounds, and 5f actinide compounds with layered crystal structures often exhibit three-dimensional multi-band Fermi surfaces, which can induce complicated spin-charge-orbital instabilities due to interplay between the two-dimensional electronic structure of the layer and the interaction between neighboring layers. The layered compounds tend to have flat cleavage surfaces which are suitable for angleresolved photoemission spectroscopy (ARPES) measurements, and the three-dimensional electronic structures can be observed by sweeping photon energy for ARPES. For example, the ARPES study on the classical 1T-TaSe 2 system has shown that the large Se-Se interaction between the layers and the strong covalency between the Ta 5d and Se 4p orbitals provide three-dimensional Fermi surfaces which play important roles in the charge density wave formation [1]. In the case of Fe-based superconductors, the origin of the spin and orbital order in the parent materials is still controversial and the three-dimensional multi-band Fermi surfaces observed by ARPES are key ingredients to understand the spin and orbital instabilities as well as the nodeless and nodal superconducting states [2]. In addition, the recent ARPES study on URu 2 Si 2 (which has the ThCr 2 Si 2 structure) has revealed that the nesting vectors in the three-dimensional momentum space are associated with the "hidden" order [3].