A new geothermal energy-assisted natural gas hydrate recovery method (GEAN) that can simultaneously exploit geothermal energy and natural gas hydrates (NGHs) by injecting water into a geothermal heat exchange well was proposed in this paper. GEAN involves no hydraulic fracturing in the geothermal reservoir and, thus, avoids the fracturing cost and decreases the damage to the geothermal reservoir. Moreover, compared with conventional thermal stimulation methods, no surface fluid heating is required. Thus, GEAN produces less carbon emissions and is more environmentally friendly. A numerical simulation model was then built to investigate the heat mining rate, the along-well water temperature, and the development performance of the hydrate-bearing layer (HBL). Finally, factors that affect the heat exchange performance were analyzed. With a geothermal reservoir temperature of 135 °C and an 1800-m-long horizontal wellbore through the geothermal reservoir, it was found that the injected water, which originally had an ambient temperature of 20 °C, returns to the HBL with a temperature of up to 89.4 °C after being heated by the geothermal heat exchange well. Moreover, the heat mining rate is over 0.3 MW throughout the production process. Therefore, the feasibility of using geothermal energy to recover NGHs by the GEAN method was proven. Compared with the depressurization method, GEAN achieved an increment cumulative gas production of 63.9%. The HBL candidate with a higher geothermal gradient is preferred due to the corresponding higher temperature of the geothermal reservoir and better heat exchange performance. The optimal water injection rate and horizontal wellbore length in the geothermal reservoir are 150 m3/d and 1800 m, respectively. Performances of the heat exchange well and HBLs could be more effectively improved by properly raising the insulation level.