Deep convolutional neural networks (CNNs) have produced remarkable outcomes in finger vein recognition. However, these networks often overfit label information, losing essential image features, and are sensitive to noise, with minor input changes leading to incorrect recognition. To address above problems, this paper presents a new classification reconstruction cycle generative adversarial network (CRCGAN) for finger vein recognition. CRCGAN comprises a feature generator, a feature discriminator, an image generator, and an image discriminator, which are designed for robust feature extraction. Concretely, the feature generator extracts features for classification, while the image generator reconstructs images from these features. Two discriminators provide feedback, guiding the generators to improve the quality of generated data. With this design of bi-directional image-to-feature mapping and cyclic adversarial training, CRCGAN achieves the extraction of essential features and minimizes overfitting. Additionally, precisely due to the extraction of essential features, CRCGAN is not sensitive to noise. Experimental results on three public databases, including THU-FVFDT2, HKPU, and USM, demonstrate CRCGAN's competitive performance and strong noise resistance, achieving recognition accuracies of 98.36%, 99.17% and 99.49% respectively, with less than 0.5% degradation on HKPU and USM databases under noisy conditions.