Remora suckerfish can attach to various marine hosts with diverse, complex surfaces using its adhesion disc pad. The remora disc can form independent compartments between adjacent lamellae when attaching to a substrate. The lamellae’s spinules can engage with the surfaces while maintaining compartments’ separate attachment. Meanwhile, the remora disc is flexible and can bend to adapt curved surfaces. The rigid skeleton structure and movement of lamellae are challenges for implementing a bio-inspired robot with independent compartments’ adhesive ability. We designed a biomimetic, multi-material flexible remora disc (87 mm long, 40mm wide) with multiple rows of lamellae that can achieve independent compartments during attachment. Then we investigated its adhesion performance on rough, curved, damaged, and protruding artificial surfaces in a lab aquarium. We found that the biomimetic suction disc can attach to rough surfaces (grain size: 50 μm) for 49.1 ± 2.1 h underwater and 4.8 ± 0.3 h in air. The disc can also attach to the curved surface (radius of curvature: 50 mm), a surface with a hole (hole diameter: 25 mm), and a bumped surface (protuberance height: 1cm) in water and air. We further developed an untethered aerial-aquatic quadrotor robot equipped with the disc prototype. The quadrotor robot can reversibly transit between air and water to rapidly adhere to complex surfaces through various highly maneuvering modes. This robot is also capable of hitchhiking on moving objects. Our results may shed light on the future aerial-aquatic robots with the adhesive ability for dry and underwater environments.