Abstract In this study, the surface of the carbon nanotubes was modified by chemical functionalization. The carbon nanotubes were placed in a mixed acid solution with a nitric acid-to-sulfuric acid volume ratio of 1:3. The results of the functionalization of the carbon nanotubes were investigated by controlling the reaction time. From the experimental results, the functionalized carbon nanotubes with a reaction time of 12 hours show good dispersibility. In the study of the essential characteristics of composite materials, it was observed that the tensile strength decreased with increase of carbon nanotube content. Compared with the result of the tensile strength test, it can be found that with increasing carbon nanotube content, the microwave heating and shape recovery speed are greatly improved. The experimental results show that the shape memory polymer composite with 4 wt% carbon nanotubes has the fastest microwave heating rate, so it takes only 2 minutes to achieve complete shape recovery. Finally, this study used shape memory polymer composites doped with 4 wt% carbon nanotubes as the driving end, combined with an elastic structure made of polyimide (PI) film using origami techniques to form a worm actuator. In the test, the system could move a distance of 6 mm forward during a microwave time of 1 minute. In addition, this research also constructed a physical model of shape memory polymer and explored the simple movement mechanism of the system.