This paper is devoted to the underwater and terrestrial locomotion aspects of an amphibious robotic fish propelled by modular fish-like propelling units and a pair of hybrid wheel-propeller-fin mechanisms. According to the mechanical structure and locomotion characteristics of the robot, a central pattern generator (CPG) network comprising coupled oscillators is employed to produce signals for swimming, crawling, as well as transitions between them. Specifically, a set of four key parameters including a tonic input drive, a direction factor, and two pitch factors is introduced to serve as input to the CPG network. Meanwhile, a finite state machine is built to trigger locomotor pattern transitions. Field tests on the amphibious patterns and autonomous water-land transition demonstrate the effectiveness of the adopted CPG-based control architecture. The latest results show that the robot attained a maximum advancing speed of 1.16 m/s (corresponding to 1.66 body lengths per second), a minimal turning radius of approximately 0.55 m (corresponding to 0.79 body lengths) on land, as well as an average rolling speed of 204 degrees per second in an alligator-like roll maneuver. It is also found that the dolphin-like dorsoventral swimming could provide an increase of 10.3% in speed compared to the fish-like carangiform swimming on the same propulsion platform.