  We present the next-to-next-to-leading order ($\alpha \alpha_s^2$)
corrections to the first moment of the polarized virtual photon structure
function $g_1^\gamma(x,Q^2,P^2)$ in the kinematical region $Q^2\gg P^2 \gg
\Lambda^2$ in QCD. We find that the $\alpha \alpha_s^2$ corrections are about
3% of the sum of the leading ($\alpha$) and the next-to-leading
($\alpha\alpha_s$) contributions, when $Q^2=30\sim 100 {\rm GeV}^2$ and $P^2=3
{\rm GeV}^2$.
