Modeling sparse and dense image matching within a unified functional correspondence model has recently attracted increasing research interest. However, existing efforts mainly focus on improving matching accuracy while ignoring its efficiency, which is crucial for real-world applications. In this paper, we propose an efficient structure named Efficient Correspondence Transformer (ECO-TR) by finding correspondences in a coarse-to-fine manner, which significantly improves the efficiency of functional correspondence model. To achieve this, multiple transformer blocks are stage-wisely connected to gradually refine the predicted coordinates upon a shared multi-scale feature extraction network. Given a pair of images and for arbitrary query coordinates, all the correspondences are predicted within a single feed-forward pass. We further propose an adaptive query-clustering strategy and an uncertainty-based outlier detection module to cooperate with the proposed framework for faster and better predictions. Experiments on various sparse and dense matching tasks demonstrate the superiority of our method in both efficiency and effectiveness against existing state-of-the-arts. Project page: https://dltan7.github.io/ecotr .