  The inclusive $J/\Psi$, $\Psi(2S)$ and $\Upsilon(1S)$ direct and resolved
photoproduction are investigated by including the quark subprocesses in the
framework of non-relativistic quantum chromodynamics (NRQCD). We find that the
theoretical total cross section of heavy quarkonium productions are in good
agreement with the data available at HERA, once the $\gamma q$, $qg$ and $qq$
subprocesses in the heavy quark pair productions are taken into account. The
inclusive diffractive rapidity and transverse momentum distributions of
$J/\Psi$, $\Psi(2S)$ and $\Upsilon(1S)$ in $pp$, $pPb$ and $PbPb$ collisions at
LHC are also studied by our quark improved NRQCD model combined with the
resolved pomeron model. We find that the contributions from the quark involved
subprocesses can reach to $8\%$ in the rapidity distribution and $6\%$ in the
transverse momentum distribution. The numerical results show that the
contributions from quark involved subprocesses are significant in heavy
quarkonium photoprodution.
