  We calculate the gluon structure function of a color dipole in
near-light-cone SU(2) lattice QCD as a function of $x_B$. The quark and
antiquark are external non-dynamical degrees of freedom which act as sources of
the gluon string configuration defining the dipole. We compute the color dipole
matrix element of transversal chromo-electric and chromo-magnetic field
operators separated along a direction close to the light cone, the Fourier
transform of which is the gluon structure function. As vacuum state in the pure
glue sector, we use a variational ground state of the near-light-cone
Hamiltonian. We derive a recursion relation for the gluon structure function on
the lattice similar to the perturbative DGLAP equation. It depends on the
number of transversal links assembling the Schwinger string of the dipole.
Fixing the mean momentum fraction of the gluons to the "experimental value" in
a proton, we compare our gluon structure function for a dipole state with four
links with the NLO \emph{MRST} 2002 and the \emph{CTEQAB-0} parameterizations
at $Q^2=1.5 \mathrm{GeV}^2$. Within the systematic uncertainty we find rather
good agreement. We also discuss the low $x_B$ behavior of the gluon structure
function in our model calculation.
