Finger-vein biometrics has attracted significant attention in recent years, posing a challenge in extracting robust finger-vein patterns from raw images with limited prior knowledge. While deep learning-based models, particularly convolutional neural network (CNN)-based methods, exhibit substantial capacity for feature representation, they still suffer from certain drawbacks. First, CNN-based models focus on learning internal feature representations by minimizing the loss function of the reconstruction error. However, this strategy may lack optimal exploration of the parameter space, resulting in limited performance. Second, existing deep learning-based feature extraction approaches encode vein textures based on an output threshold of 0.5, potentially causing the omission of discriminant vein patterns. To address these drawbacks, we propose DRL-FEE, a Deep Reinforcement Learning-based Feature Extraction and Encoding for finger-vein verification in this paper. DRL-FEE comprises a DRL-based feature extraction approach for vein texture extraction and a DRL-based supervised encoding approach for vein feature encoding. Specifically, we design a CNN model incorporated into an RL framework to establish a DRL-based segmentation model vein feature extraction, utilizing the CNN to generate a policy for feature extraction. To further enhance performance, we develop a DRL-based supervised encoding approach with a transformer-based controller to search for an optimal threshold for vein feature encoding. The experimental results on three public finger-vein databases demonstrate that the proposed DRL-FEE outperforms state-of-the-art solutions, achieving the lowest verification errors with EERs of 3.13%, 2.86%, and 1.66%, respectively.