The broad and powerful pectoral fins of manta rays are crucial to their efficient and maneuverable swimming. However, very little is currently known about the pectoral-fin-driven 3-D locomotion of manta-inspired robots. This study is focused on the development and 3-D path-following control of an agile robotic manta. First, a novel robotic manta with 3-D mobility is constructed, of which the distinctive pectoral fins provide the only propulsion. Specifically, the unique pitching mechanism is detailed in which the time-coupled coordination movement of the pectoral fins is applied. Second, based on a 6-axis force measuring platform, the propulsion characteristics of the flexible pectoral fins are analyzed. Then, the force-data-driven 3-D dynamic model is further established. Third, a control scheme combined with a line-of-sight (LOS) guidance system and a sliding-mode fuzzy controller is conceived, addressing the 3-D path-following task. Finally, various simulated and aquatic experiments are conducted, demonstrating the superior performance of our prototype and the effectiveness of the proposed path-following scheme. This study will hopefully generate fresh insights into the updated design and control of agile bioinspired robots performing underwater tasks in dynamic environments.