Estimating dense correspondences between images is a long-standing image under-standing task. Recent works introduce convolutional neural networks (CNNs) to extract high-level feature maps and find correspondences through feature matching. However,high-level feature maps are in low spatial resolution and therefore insufficient to provide accurate and fine-grained features to distinguish intra-class variations for correspondence matching. To address this problem, we generate robust features by dynamically selecting features at different scales. To resolve two critical issues in feature selection,i.e.,how many and which scales of features to be selected, we frame the feature selection process as a sequential Markov decision-making process (MDP) and introduce an optimal selection strategy using reinforcement learning (RL). We define an RL environment for image matching in which each individual action either requires new features or terminates the selection episode by referring a matching score. Deep neural networks are incorporated into our method and trained for decision making. Experimental results show that our method achieves comparable/superior performance with state-of-the-art methods on three benchmarks, demonstrating the effectiveness of our feature selection strategy.