The invention discloses a continuous sampling apparatus and a continuous sampling method for a marine natural gas hydrate. The continuous sampling apparatus comprises refrigeration equipment, a single-action rotation sampling drilling tool, a high-pressure plunger pump, air compression equipment, nitrogen production equipment, a thermal insulation and pressure retention separation device and a thermal insulation and pressure retention ore box, wherein the refrigeration equipment, the single-action rotation sampling drilling tool, the high-pressure plunger pump, the air compression equipment, the nitrogen production equipment, the thermal insulation and pressure retention separation device and the thermal insulation and pressure retention ore box are connected through pipelines, and are sequentially fixed on an exploration ship, and the single-action rotation sampling drilling tool contacts a marine natural gas hydrate stratum. According to the present invention, the high-pressure low-temperature jet flow is used as the cutting tool to drill into the stratum, the broken hydrate blocks are transported to the sea surface thermal insulation and pressure retention bin through the hydraulic lifting mode, the continuous core sampling can be achieved according to the self-protection effect, the hydrate decomposition caused by the frictional heat generation of the drilling bit can be effectively reduced, and the anti-circulation channel can be in the low temperature environment.