The embodiment of the invention discloses a robot with a memory alloy hoisting rope, and a control method and device thereof. The robot comprises a mechanical arm, a control platform, wheels and a hoisting rope device. The hoisting rope device comprises a controller, a displacement sensor and at least two memory alloy grippers. According to the robot disclosed by the embodiment of the invention, when the displacement sensor detects that the distance between the memory alloy grippers and target equipment reaches the preset distance, the control platform of the robot controls the mechanical arm to stop moving and controls an electric heating device in the controller to heat the memory alloy grippers, so that the memory alloy grippers are deformed and straightened, the distance between every two adjacent memory alloy grippers is decreased, and thus the object gripping, sleeving and other actions are achieved. The robot is simple in structure and convenient to operate, the object gripping, sleeving and other actions are achieved through the memory function of memory alloy, and due to the fact that no hydraulic drive device is adopted, the problem that oil is leaked and contaminates electrical apparatus elements is avoided.