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Hybrid-driven Underwater Glider (HUG) is a new type of underwater vehicle which integrates the functions of an Autonomous Underwater Glider (AUG) and an Autonomous Unmanned Vehicle (AUV). Although HUG has the characteristics of long endurance distance, its maneuverability still has room to be improved. This work introduces a new movement form of the neck of the underwater creature into HUG and proposes a parallel mechanism to adjust the attitude angle and displacement of the HUG’s bow, which can improve the steering maneuverability. Firstly, the influence of bow movement and rotation on the hydrodynamic force and flow field of the whole machine is analyzed by using the Computational Fluid Dynamics (CFD) method. The degree of freedom, attitude control range and movement amount of the Movable Bow Mechanism (MBM) are obtained, and then the design of MBM is completed based on these constraints. Secondly, the kinematic and dynamic models of MBM are established based on the closed vector method and the Lagrange equation, respectively, which are fully verified by comparing the results of simulation in Matlab and Adams software, then a Radial Basis Function (RBF) neural network adaptive sliding mode controller is designed to improve the dynamic response effect of the output parameters of MBM. Finally, a prototype of MBM is manufactured and assembled. The kinematic, dynamics model and controller are verified by experiments, which provides a basis for applying MBM in HUGs.