Predicting traffic speed is of importance in transportation management. Signalized road networks manifest highly dynamic speed patterns that are challenging to model and predict. We propose a hybrid deep-learning-based approach for link speed prediction, aiming at capturing heterogeneous spatiotemporal correlations between road intersections. After transforming original road networks and intersections into graphs, this approach leverages a layered graph convolution network structure to model traffic speed variations at both intersection and road network levels. The two levels are combined through a fully connected neural layer. Neural spatiotemporal attention mechanisms are applied to modulate the most relevant periodical traffic information during signal cycles. The proposed approach was evaluated using real-world speed data collected in Hangzhou City, China. Experiments demonstrate that the proposed approach can offer a scalable and effective solution for predicting short-term speed for signalized road networks.