This paper addresses the automatic colorization problem, which converts a grayscale image to a colorized one. Recent deep learning approaches can colorize automatically grayscale images. However, when it comes to different scenes which contain distinct color styles, it is difficult to accurately capture the color characteristics. In this work, we propose a fully automatic colorization approach based on Symmetric Positive Definite (SPD) Manifold Learning with a generative adversarial network (SPDGAN) that improves the quality of the colorization results. Our SPDGAN model establishes an adversarial game between two discriminators and a generator. The latter is based on ResNet architecture with few alterations. Its goal is to generate fake colorized images without losing color information across layers through residual connections. Then, we employ two discriminators from different domains. The first one is devoted to the image pixel domain, while the second one is to the Riemann manifold domain which helps to avoid color misalignment. Extensive experiments are conducted on the Places365 and COCO-stuff databases to test the effect of each component of our SPDGAN. In addition, quantitative and qualitative comparisons with state-of-the-art methods demonstrate the effectiveness of our model by achieving more realistic colorized images with less artifacts visually, and good results of PSNR, SSIM, and FID values.