  We report the measurement of the direct $CP$ asymmetry in the radiative
$\bar{B}\rightarrow X_{s+d}\gamma$ decay using a data sample of $(772 \pm
11)\times 10^6$ $B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance with
the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. The $CP$
asymmetry is measured as a function of the photon energy threshold. For
$E^{\rm{*}}_{\gamma} \geq 2.1~{\rm{GeV}}$, where $E^{\rm{*}}_{\gamma}$ is the
photon energy in the center-of-mass frame, we obtain
$\mathcal{A}_{CP}(\bar{B}\rightarrow X_{s+d}\gamma)= (2.2 \pm 3.9 \pm 0.9) \%$,
consistent with the Standard Model prediction.
