Flying insects and swimming fishes have high efficiency and high maneuverability in air and water, respectively. Their wings and fins have evolved for many ages to adapt to propelling in the complex environment. In the paper, an integrative biomimetic robotic fish is proposed and developed, which combines the advantages of insect wings and fish fins to achieve a high agility underwater. In the robotic fish, two caudal fins were equipped at the tail of the robotic fish in parallel as the main propulsion mechanism, the opposite flapping of the two caudal fins generates mutually opposing lateral forces during cruising, which leads to a stable and high-performance swimming. In addition, two pectoral fins that mimic the function of insect wings were equipped at two sides of the robotic fish, which enhances the robotic fish maneuverability in vertical plane. Moreover, a central pattern generator (CPG) model was designed to achieve the versatile maneuvering motions, motion switching, and autonomous swimming with an obstacle avoiding ability. The experiments have demonstrated that the robotic fish can swim more stably and efficiently with versatile maneuver motions by taking advantage of the integrative propulsion mechanism. The developed robotic fish have many potential applications for its agility, stable swimming, and low-cost structure.