  We report on the detection of a small overdensity of stars in velocity space
with systematically higher Galactocentric rotation velocity than the Sun by
about 20 km s$^{-1}$ in the $Gaia$ Data Release 1 Tycho-Gaia astrometric
solution (TGAS) data. We find these fast Galactic rotators more clearly outside
of the Solar radius, compared to inside of the Solar radius. In addition, the
velocity of the fast Galactic rotators is independent of the Galactocentric
distance up to $R-R_{\odot}\sim0.6$ kpc. Comparing with numerical models, we
qualitatively discuss that a possible cause of this feature is the co-rotation
resonance of the Perseus spiral arm, where the stars in peri-centre phase in
the trailing side of the Perseus spiral arm experience an extended period of
acceleration owing to the torque from the Perseus arm.
