  We calculate the first moment of the photon structure function,
$<x>^{\gamma}=\int^1_0 dx F^{\gamma}_2(x,Q^2)$, on the quenched lattices with
$\beta=6.0$ using the formalism developed by the authors recently. In this
exploratory study, we take into account only the connected contractions. The
result is compared with the experimental data as well as model predictions.
