Soft actuators that exhibit large deformation and can move at a fast speed in response to external stimuli have been in high demand for biomimetic applications. In this paper, we propose a convenient approach to fabricate a reversible and thermal-responsive composite hydrogel. Under the irradiation of visible light, the striped hydrogel can bend at a speed of up to 65.72°/s with carbon nanotubes loaded at a concentration of 3 mg/mL. A jellyfish-like miniature soft robot is made using this hydrogel. When driven by visible light, the robot can move at a maximum speed of 3.37 mm/s. Besides swimming, other motion modes, including walking and jumping, are also achieved by the robot. In addition, the robot can perform directional transportation of tiny objects. As a new actuation approach for the research of jellyfish-like miniature soft robots, this work is of great significance to the development of flexible bionic robots. Moreover, this work also offers some important insights into the research of biomimetic robots driven by visible light.