Nowadays the number of vehicles is increasing day by day and vehicle emission becomes a major pollution source. To wisely control vehicle emission, accurate vehicle emission prediction is of critical importance. However, accurate vehicle emission prediction suffers from many challenges, such as the strong nonlinearity of emission data and the temporal correlation and spatial interaction between different road segments, which become more complicated for mid- and long-term prediction. To resolve these challenging issues, we propose an attention-based global and local spatial-temporal graph convolutional network (AGLGCN) to effectively predict mid- and long-term vehicle emission through a graph structural network. The proposed AGLGCN consists of two major parts: 1) a spatial-temporal attention mechanism to effectively capture the dynamic spatial-temporal correlation of vehicle emission data by merging hourly, daily, and weekly sequences, 2) a global and local spatial graph convolution network to capture the hidden global and local spatial dependencies based on graph convolution. AGLGCN can capture the dynamic temporal correlation as well as the global and local spatial information variation of vehicle emission, and effectively predict mid- and long-term time series. Two real-world vehicle emission datasets are taken to evaluate AGLGCN. Experimental results demonstrate that our proposed AGLGCN can outperform some state-of-the-art methods.