Dynamic spatio-temporal dependencies and temporal patterns in traffic series are critical factors affecting traffic forecasting accuracy. Due to the intrinsic challenges of incorporating explicit, logical knowledge into the implicit black-box learning process of neural networks, only a few methods effectively use prior knowledge to improve the learning of traffic forecasting. To tackle this problem, we introduce a new approach called Knowledge-augmented and Time-aware Graph Convolutional Network, namely KaTaGCN. At its core, we have created a knowledge-augmented module that boosts the diffusion weights between closely related adjacent nodes in graph learning. This is achieved by implementing a new loss function. Then, to learn the periodic implicit relationship between these timestamps and traffic signals, the weights and biases are chosen adaptively to be trained based on the timestamps of each sample. Finally, a gated spatio-temporal mapping module regresses high-dimensional embedded features from spatial and temporal dimensions. KaTaGCN is structured without any attention mechanisms or recurrent neural networks. Extensive experimental results on six real-world public traffic datasets demonstrate that KaTaGCN achieves an average improvement of 4.29% in forecasting performance compared with suboptimal results.