In most of gas hydrates reservoirs, the low permeability of sediments limits the commercial production of gas hydrates. Hydraulic fracturing is an efficient way to improve the permeability in hydrate reservoirs. However, how to choose a suitable hydraulic fracturing direction during hydrate production in a 3D hydrate reservoir is still unknown. In this study, the production of gas hydrates and underlying free gas within 10 years by a depressurization horizontal well (along X-axis) under different directions (XY, YZ, XZ plane) of hydraulic fracturing was numerically studied in a 3D model. The simulation results showed that, compared with no hydraulic fracturing, the final increase ratios of the hydrate dissociation volume and gas production volume for the fracturing in XY, YZ, and XZ plane were 188.16 %, 218.96 %, 84.95 %, and 170.29 %, 253.66 %, 102.64 %, respectively, and the final increase ratios of water production amount for the fracturing in XY, YZ, and XZ plane were 140.88 %, 787.25 %, and 381.07 %, respectively. For the hydraulic fracturing in YZ plane, the connection of the production well with the upper and lower strata was earlier, and the underlying free gas was mainly produced in the early period of hydrate production, leading to the higher gas production rate and gas to water ratio in the early period. However, the gas production rate and the gas to water ratio were reduced in the later period of hydrate production due to the consumption of the underlying free gas. For the hydraulic fracturing in XY plane, the connection of the production well with the upper and lower strata was delayed, and the underlying free gas was mainly produced in the later period of hydrate production, leading to the higher gas production rate and gas to water ratio in the later period. By comprehensive consideration, for the depressurization induced hydrate production by a horizontal well along the X-axis, it's suggested that the most suitable fracturing direction should be in YZ plane for a short production period (within 5 years), and it should be in XY plane for a long production period (exceeds 5 years). This study proposes a new point that the suitable hydraulic fracturing direction is related to hydrate production period, which could provide some guidance for gas hydrates production by hydraulic fracturing.