We describe the modelling and control of a newkind airship which is propelled by buoyancy. Based on the Newton-Euler equations and Kirchhoff equations, and referred to the models of underwater gliders and aircraft, a 6DOF nonlinear mathematical model of a buoyancy-driven airship is derived, with features distributed internal mass, and no thrust, elevators and rudders. The attitudes are controlled by the motion of internal mass. The performances of the airship are studied in the vertical plane. A linear feedback controller is derived for the nonlinear model. The results of simulation display robustness properties of the controllers to disturbances.