Quadruped robots, with their biomimetic structure, are capable of stable locomotion in complex terrains and are vital in rescue, exploration, and military applications. However, developing multi-modal robots that feature simple motion control while adapting to diverse amphibious environments remains a significant challenge. These robots need to excel at obstacle-crossing, waterproofing, and maintaining stability across various locomotion modes. To address these challenges, this paper introduces a novel leg–fin integrated propulsion mechanism for a bionic quadruped robot, utilizing rapidly advancing soft materials and integrated molding technologies. The robot’s motion is modeled and decomposed using an improved central pattern generator (CPG) control network. By leveraging the control characteristics of the CPG model, global control of the single-degree-of-freedom drive mechanism is achieved, allowing smooth transitions between different motion modes. The design is verified through simulations conducted in the Webots environment. Finally, a physical prototype of the quadruped compliant robot is constructed, and experiments are carried out to test its walking, turning, and obstacle-crossing abilities in various environments. The experimental results demonstrate that the robot shows a significant speed advantage in regions where land and water meet, reaching a maximum speed of 1.03 body lengths per second (bl/s).