A guidance vector field based path-following control method for an under-actuated airship is presented. Firstly, the under-actuated airship dynamic model is established based on Newton-Euler equations. Then the guidance vector field is constructed based on the vector field theory to obtain the desired yaw angle, and the path-following controller is proposed by using backstepping technique. It is proved that the proposed controller can make the airship track the desired path and the other closed-loop states are bounded. Finally, compared with an existing method, simulation results show the effectiveness and superiority of the proposed algorithm.