For an air-breathing hypersonic vehicle with a variable geometry inlet (AHV-VGI), a movable translating cowl is used to track the shock on lip conditions to capture enough air mass flow, which can extend the velocity range and be favourable to the acceleration and manoeuvring flight. The authors firstly establish longitudinal dynamics for AHV-VGI, and consider the lumped disturbances which include the unknown external disturbance, the parameter uncertainties and the uncertainty parts introduced by translating cowl. Then, the dynamic surface control strategy based on a fuzzy disturbance observer (FDO) is proposed for AHV-VGI control. The control process for AHV-VGI is divided into two subsystems. For each subsystem, a sliding mode controller is designed, and FDOs are adopted to compensate the lumped disturbances, which can render the disturbance estimate errors convergent. Numerical simulations are presented to illustrate the effectiveness of the proposed method and the advantages of translating cowl.