Point cloud upsampling is necessary for Augmented Reality, Virtual Reality, and telepresence scenarios. Although the geometry upsampling is well studied to densify point cloud coordinates, the upsampling of colors has been largely overlooked. In this paper, we propose CU-Net, the first deep-learning point cloud color upsampling model. Leveraging a feature extractor based on sparse convolution and a color prediction module based on neural implicit function, CU-Net achieves linear time and space complexity. Therefore, CU-Net is theoretically guaranteed to be more efficient than most existing methods with quadratic complexity. Experimental results demonstrate that CU-Net can colorize a photo-realistic point cloud with nearly a million points in real time, while having better visual quality than baselines. Besides, CU-Net can adapt to an arbitrary upsampling ratio and unseen objects. Our source code will be released to the public soon.