The decomposition of marine gas hydrates is one of the important causes for the instability of submarine slopes. In order to exploit natural gas hydrate safely and efficiently, it is necessary to evaluate the stability of seabed slopes containing hydrate reservoirs scientifically. Based on the finite element strength reduction method, the stability of a submarine slope in the Shenhu area of the South China Sea is investigated, with a focus on the impact of marine gas hydrate decomposition on shear strength. The results are as follows. As the degree of decomposition of marine gas hydrate increases, the stability of the slope shows a decreasing trend. When the degree of decomposition is between 40% and 80%, the stability of the slope is sensitive to changes in the degree of hydrate decomposition. As the degree of decomposition increases, the safety factor decreases rapidly and the sliding depth of the anti-shear failure increases significantly, exceeding the position of the hydrate reservoir. A method for analyzing the stability of slopes in hydrate-bearing reservoirs has been established with finite element numerical simulation, and lays a theoretical foundation for geological risk assessment and management in the extraction of marine gas hydrate resources.