  The virtual photon structure function $g_1^{\gamma}(x,Q^2,P^2)$, which can be
obtained in polarized $e^{+}e^{-}$ colliding-beam experiments, is investigated
for $\Lambda^2 \ll P^2 \ll Q^2$, where $-Q^2$ ($-P^2$) is the mass squared of
the probe (target) photon. The analysis is made to next-to-leading order in
QCD, in the framework of the QCD improved parton model with the DGLAP evolution
equations. The non-leading corrections significantly modify the leading log
result, in particular, at large $x$ as well as at small $x$.
