Adaptive gradient algorithms borrow the moving average idea of heavy ball acceleration to estimate accurate first- and second-order moments of gradient for accelerating convergence. However, Nesterov acceleration which converges faster than heavy ball acceleration in theory and also in many empirical cases is much less investigated under the adaptive gradient setting. In this work, we propose the ADAptive Nesterov momentum algorithm, Adan for short, to speed up the training of deep neural networks effectively. Adan first reformulates the vanilla Nesterov acceleration to develop a new Nesterov momentum estimation (NME) method, which avoids the extra computation and memory overhead of computing gradient at the extrapolation point. Then Adan adopts NME to estimate the first- and second-order moments of the gradient in adaptive gradient algorithms for convergence acceleration. Besides, we prove that Adan finds an ϵ-approximate first-order stationary point within O(ϵ−3.5) stochastic gradient complexity on the nonconvex stochastic problems (e.g., deep learning problems), matching the best-known lower bound. Extensive experimental results show that Adan surpasses the corresponding SoTA optimizers on both vision transformers (ViTs) and CNNs, and sets new SoTAs for many popular networks, e.g., ResNet, ConvNext, ViT, Swin, MAE, LSTM, Transformer-XL, and BERT. More surprisingly, Adan can use half of the training cost (epochs) of SoTA optimizers to achieve higher or comparable performance on ViT and ResNet, e.t.c., and also shows great tolerance to a large range of minibatch size, e.g., from 1k to 32k. We hope Adan can contribute to the development of deep learning by reducing training cost and relieving engineering burden of trying different optimizers on various architectures.