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.
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