Behaviors of gas and water production from a gas hydrate reservoir are based on fully coupled Thermal–Hydraulic–Chemical (THC) processes in porous media. Studies using experiments and mathematical models could be improved in hydrate-bearing sediments in the laboratory. The experiment of depressurization-induced methane hydrate dissociation via a single vertical well was carried out in quartz sands in a pilot-scale hydrate simulator (PHS). The multi-stage hydrate dissociation process, including the free liquid release, well shutdown, depressurization, and constant pressure, was achieved by complex manual operation of the production well in the experiment. A full implicit simulator of hydrate (FISH), a four-component, three-phase mathematical model, was developed and employed to reproduce the hydrate dissociation experiment. The kinetics of the hydrate reaction, heat/mass transfer in porous media, and mass conservation in the pressure vessel were validated by the experimental results. The key finding of this study is the acquisition of a group of unified parameters in a suitable mathematical model that could clearly elucidate the hydrate dissociation process in all stages. The mean absolute percentage error (MAPE) values of the gas and aqueous production are, respectively, as low as 2.338 and 9.630%. The strong confidence of the accuracy of the numerical simulator has been built up after the analysis of the experiment and the numerical simulation in this study, which could be used to evaluate gas recovery from marine hydrate reservoirs.