This paper focuses on the problem of the consensus tracking control for multiple autonomous underwater vehicles(AUVs) based on a novel distributed observer. To achieve a good estimate performance of a distributed observer without knowing the leader's dynamics, firstly, using the deterministic learning theory, the uncertain nonlinearity of the leader is described by constant radial basis function(RBF) neural networks(NNs). Based on the constant RBF NNs, a novel deterministic learning-based distributed observer is proposed for multiple AUVs, and the observer error is proven to exponentially converge to a small neighborhood of the origin. By means of the observed leader's output, a distributed tracking control scheme is proposed by backstepping and dynamic surface techniques. Lyapunov stability analysis is used to prove that all the signals in the closed-loop system are bounded and the consensus tracking errors converge to a small neighborhood of the origin. Finally, a simulation example is implemented to illustrate the effectiveness of the proposed scheme.