Abstract: To realize the bottom following control for underactuated autonomous underwater vehicle(AUV),a nonlinear backstepping controller based on Lyapunov stability theory is presented.Combined with the dynamic characteristics of AUV,the bottom following error equations in the vertical plane are established based on virtual guide method.Backstepping method is adopted to design the bottom following controller,then the stability of the whole system can be analyzed by Lyapunov stability theory.Bottom profile with constant slopes is used to evaluate the performance of the bottom following controller,and AUV is set to keep a constant height to the desired bottom profile.Results show that the designed controller can achieve accurate tracking of bottom profile with constant slopes.