Model-agnostic meta-learning (MAML) is one of the most successful meta-learning algorithms. It has a bi-level optimization structure where the outer-loop process learns a shared initialization and the inner-loop process optimizes task-specific weights. Although MAML relies on the standard gradient descent in the inner-loop, recent studies have shown that controlling the inner-loop’s gradient descent with a meta-learned preconditioner can be beneficial. Existing preconditioners, however, cannot simultaneously adapt in a task-specific and path-dependent way. Additionally, they do not satisfy the Riemannian metric condition, which can enable the steepest descent learning with preconditioned gradient. In this study, we propose Geometry-Adaptive Preconditioned gradient descent (GAP) that can overcome the limitations in MAML; GAP can efficiently meta-learn a preconditioner that is dependent on task-specific parameters, and its preconditioner can be shown to be a Riemannian metric. Thanks to the two properties, the geometry-adaptive preconditioner is effective for improving the inner-loop optimization. Experiment results show that GAP outperforms the state-of-the-art MAML family and preconditioned gradient descent-MAML (PGD-MAML) family in a variety of few-shot learning tasks. Code is available at: https://github.com/Suhyun777/CVPR23-GAP.