Gluon density and its distributions inside nuclei and the parton modification of bounded nucleons inside a nucleus, are some of the main standing problems in nuclear and particle physics. In recent years, ultra-peripheral collisions (UPC) of heavy ions have provided a new way of probing the gluon density, which is based on coherent diffractive vector-meson productions, e.g., $J/\psi$ meson. For heavy ions, e.g., Pb, the gluon density is found to be significantly suppressed through the UPC $J/\psi$ measurement, suggesting a strong gluon shadowing effect in heavy nuclei. In this analysis, we aim to look at a unique set of data taken by the STAR experiment, where $J/\psi$ mesons are photoproduced off the deuteron target with no other particle produced, except for the deuteron or its breakup products. The Zero Degree Calorimeter response with respect to the deuteron dissociation by detecting a beam-rapidity neutron is also investigated and provides additional information about the underlying physics process. The cross section of $J/\psi$ photoproduction in the photon-deuteron system is measured at the photon-nucleon center-of-mass energy $W\sim25~\rm{GeV}$, as well as the momentum transfer $t$ dependence cross section, $d\sigma/dt$. Data suggests a wider gluon density distribution than the Hulthen charge density distribution in deuteron.