This paper presents a biomimetic robotic fish that swims using thunniform kinematics for advanced underwater mobility. Propulsion and maneuvering of the robotic fish are achieved with a lunate caudal fin that undergoes combined translational and rotational motion. A parallel four-bar propulsive mechanism attached to the rear of the rigid torpedo-shaped body is used to deliver motor rotation to the caudal fin. Oscillatory control signals for the tail joints are generated with a CPG controller composed of two unidirectionally coupled Hopf oscillators. Coupling terms that allow direct specification of phase relation between oscillators are formulated. The maximum speed of the robotic fish can reach 2.0 m/s and excellent maneuverability has been exhibited. The outstanding swimming performances present exciting possibilities for real-world deployment of the robotic fish.