  Real magnetic and lattice deformation gauge fields have been investigated in
honeycomb lattice of graphene. The coexistence of these two gauges will induce
a gap difference between two valley points ($K$ and $K'$) of system. This gap
difference allows us to study the possible topological valley Hall current and
valley polarization in the graphene sheet. In the absence of magnetic field,
the strain alone could not generate a valley polarization when the Fermi energy
coincides exactly with the Dirac points. Since in this case there is not any
imbalance between the population of the valley points. In other words each of
these gauges alone could not induce any topological valley-polarized current in
the system at zero Fermi energy. Meanwhile at non-zero Fermi energies
population imbalance can be generated as a result of the external strain even
at zero magnetic field. In the context of Berry curvature within the linear
response regime the valley polarization (both magnetic free polarization,
$\Pi_0$, and field dependent response function, $\chi_\alpha$) in different
values of gauge fields of lattice deformation has been obtained.
