In this work, we first characterize the hybrid execution patterns of GCNs on Intel Xeon CPU. Guided by the characterization, we design a GCN accelerator, HyGCN, using a hybrid architecture to efficiently perform GCNs. Specifically, first, we build a new programming model to exploit the fine-grained parallelism for our hardware design. Second, we propose a hardware design with two efficient processing engines to alleviate the irregularity of Aggregation phase and leverage the regularity of Combination phase. Besides, these engines can exploit various parallelism and reuse highly reusable data efficiently. Third, we optimize the overall system via inter-engine pipeline for inter-phase fusion and priority-based off-chip memory access coordination to improve off-chip bandwidth utilization. Compared to the state-of-the-art software framework running on Intel Xeon CPU and NVIDIA V100 GPU, our work achieves on average 1509$\times$ speedup with 2500$\times$ energy reduction and average 6.5$\times$ speedup with 10$\times$ energy reduction, respectively.