To address the challenges of sinking, imbalance, and complex control systems faced by hexapod robots walking on lunar soil, this study develops an umbrella-shaped foot lunar exploration hexapod robot. The overall structure of the robot is designed to mimic the body structure of insects. By incorporating a four-bar linkage mechanism to replace the commonly used naked joints in traditional hexapod robots, the robot reduces the number of degrees of freedom and simplifies control complexity. Additionally, an extension mechanism is added to the robot’s foot, unfolding into an umbrella shape to provide a larger support area, effectively addressing the issue of foot sinking instability during walking. This study adopts and simplifies the Central Pattern Generator (CPG) model to generate stable periodic control signals for the robot’s legs. Precise control of the extension mechanism’s unfolding period is achieved through mapping functions. A joint simulation platform using Solid Works and Matlab is established to analyze the stability of the robot’s walking. Finally, walking experiments are conducted on the prototype, confirming the smooth walking of the lunar exploration hexapod robot. The results indicate that the designed lunar exploration hexapod robot has a reasonable structure, excellent stability in motion, and the CPG control scheme is feasible.