Natural gas hydrate is a promising source of energy and are widely distributed in ocean continental shelves and permafrost horizons. Reservoir permeability is one of the most important factors for hydrate development. Compared to a conventional hydrocarbon reservoir, the permeability of a hydrate reservoir is more susceptible to overburden pressure due to the variations of hydrate saturation and pore structure induced by the phase transformation between solid and fluid during hydrate exploitation. In this investigation, experimental devices were designed to study the influencing factors of hydrate-bearing reservoir permeability under overburden pressure, which was replicated by applying confining pressure around the samples. The corresponding permeability was calculated according to different confining pressure, initial pore pressure and hydrate saturation. The results indicated that under the same confining pressure, reservoir permeability decreased nonlinearly with increased hydrate saturation. The confining pressure could change the deposit compaction and hydrate stability conditions resulting in a negative effect on reservoir permeability. Initial pore pressure was considered an influencing factor that could weaken the effect of confining pressure. The increase and decrease of confining pressure displayed contrasting impacts on hydrate reservoir permeability, and the increase of confining pressure showed a larger impact on permeability than the decrease of pressure. Based on the Masuda model, we conducted experimental data analysis and established a new empirical equation considering the confining pressure, initial pore pressure and hydrate saturation. This equation could improve the accuracy of permeability prediction and provide theoretical support for natural gas hydrate production.