The invention discloses a multi-degree-of-freedom flexible dexterous hand based on a shape memory alloy. The multi-degree-of-freedom flexible dexterous hand comprises a wrist bone, a thumb, an index finger, a middle finger, a ring finger, a little finger and a joint mechanism, wherein each finger comprises a metacarpal bone and a bendable section coated with a flexible material, the bendable section of the thumb is fixed on a connector and directly connected with the metacarpal bone, the metacarpal bone of the thumb and the wrist bone are connected by utilizing a cross-shaft joint, the two rotating degrees of freedom for the forward and lateral swinging of the thumb are achieved, the bendable sections of the other four fingers are fixed on the connector, are connected with the corresponding metacarpal bones through rotating-shaft joints, and have the rotating degree of freedom for lateral swinging, and the metacarpal bone of the four fingers are directly and fixedly connected onto thewrist bone; through the heating arrangement of the shape memory alloy inside the bendable sections and on the lateral surfaces of the fingers, the bendable section are driven to bend and deform as well as the joints are driven to swing; and through one or more flexible sensor arrays that cling to the surfaces of the fingers, the bending and swinging angles of all the fingers can be detected. The multi-degree-of-freedom flexible dexterous hand is simple in structure, is low in cost, and can be applied to the fields of artificial limbs, manipulators and the like.