Compared with the gradient descent, the adaptive gradient descent (AdaGrad) keeps the geometric information of historical data by using the arithmetic average of squared past gradients, and obtains tighter convergence bounds when copingwith sparse data. On the other hand, by adding the momentum term to gradient descent, Nesterov’s accelerated gradient (NAG) not only obtains order of magnitude accelerated convergence for solving smooth convex optimization problems, but also achieves the optimal individual convergence rate for non-smooth convex problems. Recently, there have been studies on the combination of adaptive strategy and NAG. However, as a typical adaptive NAG algorithm, AcceleGrad fails to reflect the distinctions between dimensions due to using different adaptive variant from AdaGrad, and it only obtains the weighted averaging convergence rate. So far, there still lacks the theoretical analysis of individual convergence rate. In this study, an adaptive NAG method, which inherits AdaGrad’s step size setting, is proposed. It is proved that the proposed algorithm attains the optimal individual convergence rate when solving the constrained non-smooth convex optimization problems. The experiments are conducted on the typical optimization problem of hinge loss function for classification and L1 loss function for regression with L1 norm constraint, and experimental results verify the correctness of the theoretical analysis and superior performance of the proposed algorithm over AcceleGrad.