The work aims to overcome the problems that the color space conversion method based on deep learning requires a large number of samples and high cost of sample collection. Based on colorimetry and deep learning methods, a Cor-WGAN model that integrates multi-channel correction was proposed. A multi-stage training method was designed. The conversion relationship from RGB to CIELab color space under the condition of small samples was learned. First, the conversion effect of the model in the standard color space was tested. Then non-standard color space simulation experiments and inverse conversion experiments were designed to test the effect of the model in practical applications. The experimental results showed that the Cor-WGAN model proposed in this paper had strong small sample learning ability, and could achieve a good conversion effect under the training condition of 64 evenly distributed samples. The average color difference of conversion was 1.71, and the minimum color difference reached 0.16. More than 90% of the sample points could reach the conversion level that the human eye could not distinguish the color difference. The algorithm in this paper has obvious advantages in processing small sample color space conversion tasks, and provides a new idea for color management applications based on deep learning.