  Based on a perturbative theory of quantum chromodynamics and non-relativistic
quark model, associated $J/\psi$ plus open charm photoproduction on charm
quarks in a proton via partonic subprocess $\gamma c\to J/\psi c$ is discussed.
It is shown that the value and energy dependence of the cross section for such
process remarkably depends on the choice of charm distribution function in a
proton. In the region of small $z=E_J/E_{\gamma}<0.2$ the contribution of the
$\gamma c\to J/\psi c$ subprocess in the inelastic $J/\psi$ photoproduction
spectra is larger than the contribution of the photon-gluon fusion subprocess.
At the energy range of HERA collider intrinsic charm contribution in the total
inclusive $J/\psi$ photoproduction cross section may be equal to 4\% of the
dominant contribution of photon-gluon fusion mechanism.
