In this paper, the non-uniform illumination enhancement problem of underwater images under the artificial light sources conditions is investigated based on Convolution Neural Network (CNN). First, we propose a trainable end-to-end enhancer called NUIENet, for enhancing the non-uniform illumination of underwater images. The proposed model consists of correction network and fusion layers. The correction network adopts the encoder-decoder structure with skip connections to enhance the features of different channels in the HSV domain, and then these enhanced features are fused by the fusion layers to obtain the desired high-quality images. Second, we built an underwater images dataset using Generative Adversarial Network (GAN) and Gaussian Function. Finally, both qualitative and quantitative experimental results show that the proposed method can produce better performance compared to other state-of-the-art enhancement methods on both real-word and synthetic underwater dataset.