First-order optimization methods are currently the mainstream in training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by employing the diagonal matrix preconditioning of the stochastic gradient during the training. Despite their widespread, second-order optimization algorithms exhibit superior convergence properties compared to their first-order counterparts e.g. Adam and SGD. However, their practicality in training DNNs is still limited due to increased per-iteration computations compared to the first-order methods. We present AdaFisher--an adaptive second-order optimizer that leverages a diagonal block-Kronecker approximation of the Fisher information matrix for adaptive gradient preconditioning. AdaFisher aims to bridge the gap between enhanced convergence/generalization capabilities and computational efficiency in second-order optimization framework for training DNNs. Despite the slow pace of second-order optimizers, we showcase that AdaFisher can be reliably adopted for image classification, language modeling and stands out for its stability and robustness in hyper-parameter tuning. We demonstrate that AdaFisher outperforms the SOTA optimizers in terms of both accuracy and convergence speed. Code is available from https://github.com/AtlasAnalyticsLab/AdaFisher.