The invention discloses a strong and tough self-repairing double-response shape memory polylactic acid-based composite material and a preparation method thereof. The composite material has a formula comprising the following raw materials in parts by mass: 30-80 parts of polylactic acid, 20-70 parts of epoxidized natural rubber, 10-150 parts of ferroferric oxide, 0.2-1 part of an antioxidant, 0.5-3parts of a vulcanizing agent and 0.1-2.5 parts of a co-crosslinking agent; during preparation, the ferroferric oxide and the epoxidized natural rubber are mixed evenly first to obtain ENR/Fe3O4 grossrubber, then the polylactic acid and the antioxidant are mixed evenly through shearing, the ENR/Fe3O4 gross rubber is added, and the vulcanizing agent and the co-crosslinking agent are added after the mixture is uniform. The polylactic acid-based composite material prepared by the method provided by the invention simultaneously has self-repairing performance, soft magnetic performance, thermallyinduced shape memory performance and magnetically-induced shape memory performance, also has the characteristic of balanced toughness and strength, realizes remote control heating, and can be used inplaces such as human bodies that cannot be directly heated.