3D Skeleton-based human action recognition has attracted increasing attention in recent years. Most of the existing work focuses on supervised learning which requires a large number of labeled action sequences that are often expensive and time-consuming to annotate. In this paper, we address self-supervised 3D action representation learning for skeleton-based action recognition. We investigate self-supervised representation learning and design a novel skeleton cloud colorization technique that is capable of learning spatial and temporal skeleton representations from unlabeled skeleton sequence data. We represent a skeleton action sequence as a 3D skeleton cloud and colorize each point in the cloud according to its temporal and spatial orders in the original (unannotated) skeleton sequence. Leveraging the colorized skeleton point cloud, we design an auto-encoder framework that can learn spatial-temporal features from the artificial color labels of skeleton joints effectively. Specifically, we design a two-steam pretraining network that leverages fine-grained and coarse-grained colorization to learn multi-scale spatial-temporal features.In addition, we design a Masked Skeleton Cloud Repainting task that can pretrain the designed auto-encoder framework to learn informative representations. We evaluate our skeleton cloud colorization approach with linear classifiers trained under different configurations, including unsupervised, semi-supervised, fully-supervised, and transfer learning settings. Extensive experiments on NTU RGB+D, NTU RGB+D 120, PKU-MMD, NW-UCLA, and UWA3D datasets show that the proposed method outperforms existing unsupervised and semi-supervised 3D action recognition methods by large margins and achieves competitive performance in supervised 3D action recognition as well.