We carry out the study of the medium modification of $\gamma$-jet fragmentation function in relativistic heavy-ion collisions. To simultaneously do simulation of both jet transport and the dynamical evolution of the bulk medium, we develop CoLBT-hydro model--Coupled Linear Boltzmann Transport (LBT) and (3+1)D relativistic hydrodynamics model in real time. The lost energy and momentum by propagating jet shower partons via collisional and radiative processes are deposited into the medium and update the surrounding bulk medium for the subsequent jet transport. We use the model to calculate $\gamma$-jet fragmentation function in a function of $\xi^{jet}$ and $\xi^{\gamma}_{T}$ in Pb+Pb collisions at 5.02A TeV for different centralities, and the corresponding medium modification function in comparison with p+p collisions generated by Pythia8. The CoLBT-hydro results show the centrality dependence of the enhancement of high $p_{T}$ hadrons and the enhancement of low $p_{T}$ hadrons inside jets due to parton energy loss and jet-induced medium excitation.