Finger vein recognition technology captures subcutaneous venous structures through near-infrared imaging, offering advantages such as contactless operation and liveness detection. However, its imaging quality is susceptible to environmental illumination interference. Traditional denoising and enhancement techniques can only handle minor illumination fluctuations and fail under extreme lighting variations. Existing methods rely on multi-illumination training data or synthetic samples, which face limitations in data acquisition difficulty or inadequate generalization capability. To address these challenges, this paper proposes a Multi-Illumination Normalization finger vein recognition Network (MIN-Net) that performs recognition after normalizing complex illumination images. Firstly, the designed multi-illumination normalization generator decouples illumination information and vein structure features through the illumination and the feature coding sub-networks, which are then fused by a multi-level fusion module; Then, multiple parallel branches with deep residual blocks are added to enhance the multi-scale feature representation; Finally, an improved identity loss combined with a novel frequency-domain loss to suppress irrelevant background interference. To further investigate vein recognition under complex illumination and validate the proposed method, we constructed the Multi-Illumination Finger Vein (MIFV) dataset containing diverse illumination variations. Experimental results on both public datasets and the new MIFV dataset demonstrate that MIN-Net significantly outperforms state-of-the-art methods across all objective evaluation metrics.