Extrapolation on Temporal Knowledge Graphs presents a critical challenge, driven by its applications in predicting future events by analyzing historical data. While recent methods leverage graph structure and temporal dynamics, they often struggle to prioritize neighborhood messages and capture evolving temporal attributes at local and global scales. To address these issues, we introduce a novel forecasting architecture, named Graph Convolution Transformer, which incorporates a time-aware self-attention mechanism. Our approach integrates a Fact Graph Transformer to structure historical data and a Temporal Transformer with advanced position encoding for enhanced time series representation. Also, we propose Query-ConvTransE in the decoder to handle query-based data. Extensive evaluations across six benchmark datasets demonstrate that the model outperforms prior approaches, improving the Mean Reciprocal Rank metric by roughly 2% to 3%, with a notable advancement of 5.23% on the GDELT dataset experiment.