The invention discloses a continuum transmission mechanism-based under-actuated prosthetic hand, which comprises a motor driving unit, a continuum transmission mechanism and a mechanical hand, wherein the continuum transmission mechanism comprises a fixing plate, a plurality of fixing pipes, a plurality of guide pipes, a base, a plurality of driven wires, spacing discs and a locking disc; the motor driving unit comprises motors, output mechanisms and a plurality of driving wires; the mechanical hand comprises a palm and five fingers; each finger is provided with a plurality of knuckles; the rotation of the motors can be converted into the linear movement of the driving wires through the output mechanisms, and the continuum transmission mechanism can be driven to be deformed by the linear movement of the driving wires to move the driven wires of which one end of each is fixed with the locking disc, so that each finger of the mechanical hand is driven to finish corresponding actions. According to the continuum transmission mechanism-based under-actuated prosthetic hand, the use of a conventional rigid kinematic pair such as a hinge and a connecting rod is avoided, so that the system hysteresis is effectively eliminated, and the weight of the prosthetic hand is reduced; a great number of elastic alloy wires are used, so that the prosthetic hand is high in adaptability.