Asynchronous Byzantine Fault Tolerant (BFT) consensus protocols have garnered significant attention with the rise of blockchain technology. A typical asynchronous protocol is designed by executing sequential instances of the Asynchronous Common Sub-seQuence (ACSQ). The ACSQ protocol consists of two primary components: the Asynchronous Common Subset (ACS) protocol and a block sorting mechanism, with the ACS protocol comprising two stages: broadcast and agreement. However, current protocols encounter three critical issues: high latency arising from the execution of the agreement stage, latency instability due to the integral-sorting mechanism, and reduced throughput caused by block discarding. To address these issues,we propose Falcon, an asynchronous BFT protocol that achieves low latency and enhanced throughput. Falcon introduces a novel broadcast protocol, Graded Broadcast (GBC), which enables a block to be included in the ACS set directly, bypassing the agreement stage and thereby reducing latency. To ensure safety, Falcon incorporates a new binary agreement protocol called Asymmetrical Asynchronous Binary Agreement (AABA), designed to complement GBC. Additionally, Falcon employs a partial-sorting mechanism, allowing continuous rather than simultaneous block committing, enhancing latency stability. Finally, we incorporate an agreement trigger that, before its activation, enables nodes to wait for more blocks to be delivered and committed, thereby boosting throughput. We conduct a series of experiments to evaluate Falcon, demonstrating its superior performance.