We calculate the first moment of the photon structure function, <x > (gamma
)=integral (1)(0)dxF(2)(gamma)(x,Q(2)), on the quenched lattices with beta
= 6.0 using the formalism developed by the authors recently. In this explor
atory study, we take into account only the connected contractions. The resu
lt is compared with the experimental data as well as model predictions.