Marine methane hydrate is considered to be one of the future energy sources with the most potential due to its tremendous reserves. Permeability is a key parameter affecting the recovery efficiency and gas recovery of gas hydrate. We studied the dependence of gas permeability on hydrate saturation and effective stress using remolded core from the South China Sea. The results show that, with increasing hydrate saturation, the gas permeability first decreases, then increases, and decreases finally, which may be due to the combined effect of the growth habit of hydrates in the pores, the interaction between hydrates and particles, and the effect of effective stress. The formation and decomposition of hydrates in the sediment will cause a decrease in gas permeability. When hydrate saturation is 40.66%, the gas permeability decreases by 13 times due to hydrate formation. The gas permeability presents an approximate linear negative relationship with effective stress. The presence of hydrate significantly reduces the stress sensitivity of the sediment. A stress-sensitive critical saturation between 36.60 and 40.66% makes the ratio of permeability change to effective stress change close to a constant. This work bridges the gap of gas permeability of marine sediments between laboratory samples and natural sediments, providing reliable seepage parameters for the numerical simulation of marine hydrate exploration.