We present the discovery of an extremely-luminous dust-obscured galaxy (DOG) at z spec = 3.703, WISE J101326.25+611220.1. This DOG is selected as a candidate of extremely-luminous infrared (IR) galaxies based on the photometry from the Sloan Digital Sky Survey and Wide-field Infrared Survey Explorer. In order to derive its accurate IR luminosity, we perform follow-up observations at 450 and 850 µm using the Submillimetre Common User Bolometer Array 2 on the James Clerk Maxwell Telescope, and at 870 and 1300 µm using the Submillimeter Array, which enable us to pin down its IR Spectral Energy Distribution (SED). We perform SED fitting using 14 photometric data (0.4 -1300 µm) and estimate its IR luminosity, L IR (8-1000 µm), to be 2.2 +1.5 −1.0 ×10 14 L ⊙ , making it one of the most luminous IR galaxies in the Universe. The energy contribution from an active galactic nucleus (AGN) to the IR luminosity is 94 +6 −20 %, which indicates it is an AGN-dominated DOG. On the other hand, its stellar mass (M * ) and star formation rate (SFR) are log (M * /M ⊙ ) = 11.2 +0.6 −0.2 and log (SFR/M ⊙ yr −1 ) = 3.1 +0.2 −0.1 , respectively, which means that this DOG can be considered as a starburst galaxy in M * -SFR plane. This extremely-luminous DOG shows significant AGN and star forming activity that provides us an important laboratory to probe the maximum phase of the co-evolution of galaxies and supermassive black holes.