  Recently, significant enhancements of J/$\psi$ production at very low
transverse momenta were observed by the ALICE and STAR collaboration in
peripheral hadronic A+A collisions. The anomaly excesses point to evidence of
coherent photon-nucleus interactions in violent hadronic heavy-ion collisions,
which were conventionally studied only in ultra-peripheral collisions. Assuming
that the coherent photoproduction is the underlying mechanism which is
responsible for the excess observed in peripheral A+A collisions, its
contribution in p+p collisions with nuclear overlap, i.e.
non-single-diffractive collisions, is of particular interest. In this paper, we
perform a calculation of exclusive J/$\psi$ photoproduction in
non-single-diffractive p+p collisions at RHIC and LHC energies base on the pQCD
motivated parametrization from world-wide experimental data, which could be
further employed to improve the precision of phenomenal calculations for
photoproduction in A+A collisions. The differential rapidity and transverse
momentum distributions of J/$\psi$ from photoproduction are presented. In
comparison with the J/$\psi$ production from hadronic interactions, we find
that the contribution of photoproduction is negligible.
