  We present the discovery of an extremely-luminous dust-obscured galaxy (DOG)
at $z_{\rm spec}$ = 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 $\mu$m using the Submillimetre Common User Bolometer Array 2 on
the James Clerk Maxwell Telescope, and at 870 and 1300 $\mu$m 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 $\mu$m) and estimate its IR luminosity, $L_{\rm IR}$ (8-1000 $\mu$m), to
be $2.2^{+1.5}_{-1.0}$ $\times 10^{14}$ $L_{\odot}$, 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 $\log \,(M_\ast/M_{\odot})$ =
$11.2^{+0.6}_{-0.2}$ and $\log \,({\rm SFR}/M_{\odot}\,{\rm yr}^{-1}$) =
$3.1^{+0.2}_{-0.1}$, 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.
