DAG-based Byzantine Fault Tolerant protocols have gained popularity due to their high throughput, but they often suffer from high latency caused by the serial wave-execution model. In this paper, we propose FastDAG, the first asynchronous DAG-based consensus protocol that adopts a parallel wave-execution model. FastDAG introduces a double-layer DAG structure to parallelize voting and a cross-referencing approach to link the two layers, significantly reducing latency. To address the challenges of inconsistency between the two layers, we design a Cross-Reference Fast commit approach that determines block commitment based on voting results from both layers. To address the challenge of Byzantine behavior of the leader, we design a planned-and-forced switching approach. Real-world experiment results on 46 cloud servers show that FastDAG outperforms existing protocols, achieving 22.5% lower latency than GradedDAG [1] and 35% lower than Tusk [2].