The underwater images obtained by optical sensor such as camera have low visibility and color distortion by underwater environments. In order to enhance visibility and color of underwater images, AE(Auto-Encoder) model based CNN(Convolutional Neural Network) is mainly used recently. In this paper, we propose the AE model which is effective for visibility enhancement and color correction of underwater images. The proposed UAE(Underwater Auto-Encoder) enhances underwater images by connecting skip-connection between encoder and decoder. For training UAE, we use underwater dataset consisted of no-distorted images and distorted underwater images generated by underwater image formation modeling equation. In order to verify the performance of UAE, we compare with traditional methods for underwater image enhancement. As a result of comparison using test dataset, UAE quantitatively outperforms than traditional methods on full reference metrics consisted of PSNR, SSIM, and color difference. Also UAE is qualitatively effective on actual underwater images.