The invention discloses a legged jump robot based on piezoelectric drive and a control method thereof. The robot comprises a flexible body formed by folding four layers of planar PVC film and four piezoelectric bimorph pins, wherein the PVC film layers are connected with bounce legs, stop pieces, shape memory alloy springs and stainless steel springs. By utilizing the vibration of the piezoelectric bimorphs under the effect of sine and cosine voltages, the robot can perform straight-line walking. By utilizing the heating construction performance of shape memory alloy, the PVC layers store andrelease strain energy to achieve folding and unfolding of the bounce legs, the robot can obliquely and upward jump and be repristinated for continuous walking, and mutual switching of motion modes isachieved. The legged jump robot integrates the advantages of quick response of piezoelectric drive, high precision and large deformation of shape memory alloy, linear and jumping motions of the robotare achieved, and the application field and motion range of the piezoelectric robot are widened.