Video scene graph generation (VidSGG) aims to identify objects in visual scenes and infer their relationships for a given video. It requires not only a comprehensive understanding of each object scattered on the whole scene but also a deep dive into their temporal motions and interactions. Inherently, object pairs and their relationships enjoy spatial co-occurrence correlations within each image and temporal consistency/transition correlations across different images, which can serve as prior knowledge to facilitate VidSGG model learning and inference. In this work, we propose a spatial-temporal knowledge-embedded transformer (STKET) that incorporates the prior spatial-temporal knowledge into the multi-head cross-attention mechanism to learn more representative relationship representations. Specifically, we first learn spatial co-occurrence and temporal transition correlations in a statistical manner. Then, we design spatial and temporal knowledge-embedded layers that introduce the multi-head cross-attention mechanism to fully explore the interaction between visual representation and the knowledge to generate spatial- and temporal-embedded representations, respectively. Finally, we aggregate these representations for each subject-object pair to predict the final semantic labels and their relationships. Extensive experiments show that STKET outperforms current competing algorithms by a large margin, e.g., improving the mR@50 by 8.1%, 4.7%, and 2.1% on different settings over current algorithms.