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In this study, nonsingular modeling and cross-domain trajectory tracking control problems for a special class of coaxial hybrid aerial–underwater vehicles (HAUVs) are investigated. Coaxial HAUVs need to effectively overcome the influence of hydrodynamic factors when moving underwater, so the attitude angle required by coaxial HAUVs is much larger than that in the air. The attitude representation based on quaternion modeling is adopted to avoid the inherent singularity of Euler angle modeling. A cascade sliding mode control and proportion differentiation (SMC-PD) controller is proposed, which is used to position trajectory and attitude quaternion tracking control, respectively. An adaptive sliding mode controller based on disturbance observer (DO) enhancement is adopted in the outer loop to carry trajectory tracking control. At the same time, the expected attitude angle is calculated by the outer loop (position) and is converted into the expected quaternion. With reference to the idea of enhanced robustness in active disturbance rejection control (ADRC), a feedforward proportion derivation (PD) controller based on DO enhancement is used to track the desired quaternion. A variable parameter adaptive algorithm based on the learning rate is introduced in the cascaded SMC-PD controller. The error convergence speed of the system is further improved by adaptively changing the controller parameters. The stability of the proposed control scheme is proved by using the Lyapunov theory. The numerical simulation results show that the controller has good robustness and effectiveness. [ABSTRACT FROM AUTHOR]