Asynchronous Byzantine Fault Tolerance (BFT) reliable broadcast serves as a core component in constructing asynchronous BFT consensus algorithms, which are crucial to blockchain technology. Despite its significant role in the blockchain domain, BFT reliable broadcast still exhibits relatively high communication complexity. We propose a novel reliable broadcast protocol tailored for asynchronous network environments, leveraging Directed Acyclic Graph (DAG) technology to reduce communication complexity. Processes in the new protocol are responsible for sending response messages when they receive a broadcast message. These response messages contain both the broadcast message and references to previously received response messages, thereby forming a DAG of response messages. By analyzing the referencing patterns of response messages in the graph, the process can determine whether a message can be delivered. Under the condition of continuously receiving new broadcast messages, we show that the protocol satisfies agreement, integrity, and validity, achieving reliable broadcast. Comparative results reveal that it exhibits the lowest amortised communication complexity and amortised number of communication rounds for each broadcast message.