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Stimuli-responsive polymers and gels have been applied to biomimetic actuators or artificial muscles. Biomimetic robots using such materials can move like a living creature. Especially, electroactive polymers are said to be promising materials as advanced soft actuators. Its mechanical motion is controlled by external stimuli such as a change in solvent composition, pH, temperature and electric field etc. On the other hand, many living organisms generate an autonomous motion without external driving stimuli. In this paper, we report a novel biomimetic gel actuator that can bend and stretch with worm-like motion spontaneously without external driving stimuli. The gel actuator converts the chemical energy of oscillating reaction, i.e., the Belouzov-Zhabotinsky (BZ) reaction into the kinetic energy inside the gel. Although the gel is completely composed of synthetic polymer, it shows autonomous motion as if it is alive. To cause anisotropic contraction with curvature changes, the gel strip with gradient structure was prepared. Furthermore, the gel can walk with repeated bending and stretching motion by itself like a looper by coupling with ratchet mechanism. The "self-walking" gel actuator will create a new framework of biomimetic chemical robot.