Image bit-depth is the number of bits for each color channel of a pixel in an image which determines the number of expressable colors in an image. Although many modern displays support unprecedented higher bit-depth to show more realistic and natural colors with a high dynamic range, most media sources are still in bit-depth of 8 or lower. Since insufficient bit-depth may generate annoying false contours or lose detailed visual appearance, bit-depth expansion (BDE) from low bit-depth (LBD) images to high bit-depth (HBD) images becomes more and more important. In this paper, we adopt a learning-based approach for BDE and propose a novel CNN-based bit-depth expansion network (BitNet) that can effectively remove false contours and restore visual details at the same time. We have carefully designed our BitNet based on an encoder-decoder architecture with dilated convolutions and a novel multi-scale feature integration. We have performed various experiments with four different datasets including MIT-Adobe FiveK, Kodak, ESPL v2, and TESTIMAGES, and our proposed BitNet has achieved state-of-the-art performance in terms of PSNR and SSIM among other existing BDE methods and famous CNN-based image processing networks. Unlike previous methods that separately process each color channel, we treat all RGB channels at once and have greatly improved color restoration. In addition, our network has shown the fastest computational speed in near real-time.