This article investigates the adaptive learning control problem for a class of nonlinear autonomous underwater vehicles (AUVs) with unknown uncertainties. The unknown nonlinear functions in the AUVs are approximated by radial basis function neural networks (RBFNNs), in which the weight updating laws are designed via gradient descent algorithm. The proposed gradient descent-based control scheme guarantees the semiglobal uniform ultimate boundedness (SUUB) of the system and the fast convergence of the weight updating laws. In order to reduce the computational burden during the backstepping control design process, the command-filter-based design technique is incorporated into the adaptive learning control strategy. Finally, simulation studies are given to demonstrate the effectiveness of the proposed method.