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The development of hybrid unmanned aerial underwater vehicles (HAUVs) compatible with the advantages of the aerial vehicles and the underwater vehicles is of great significance. This paper presents the first study on a new HAUV layout using four rotors to realize the medium crossing motion of a transverse slender body similar to the fuselage of a missile or a submarine, that is, the hybrid aerial underwater quadrotor (HAUQ). Then, a robust control strategy is proposed for the take-off HAUQ on the water in the presence of unknown disturbances and complex model dynamic uncertainties. As a semi-submersible HAUQ rises straight from the water, the inside of the slender fuselage placed horizontally is filled with water. The center of the mass, the moment of inertia, and the arm of the force of the HAUQ will change rapidly in the take-off phase from the water because of the rapid nonuniform change in mass caused by the passive fast drainage. It is difficult to establish an accurate mathematical model of the complex dynamic changes caused by the multi-media dynamics, the fast changing buoyancy, and the added mass crossing the air–water surface. Therefore, an uncertain kinematic and dynamic model is established through the passive, fast, nonuniform change and the complex dynamics are considered as the unknown terms, and the external disturbances of gust and other factors are assumed as the bounded disturbance input. A robust design approach is introduced to deal with the fast time-varying mass disturbance based on the input-to-state stability (ISS) theorem. The complex dynamics are estimated using the basis function and the unknown weight parameters, and the adaptive laws are adopted for the on-line estimation of the unknown weight parameters. Considering the residual disturbance of the uncertain nonlinear system as a total disturbance term, a disturbance observer is introduced for disturbance observation. The numerical simulation shows the feasibility and robustness of the proposed algorithm.