Owing to the limited network resources in ad hoc networks, improving network throughput is the key to solve network congestion and increase network transmission efficiency. Back‐pressure routeing, as an optimal routeing strategy for throughput, has recently received substantial attention for joint routeing and scheduling over multi‐hop wireless networks. However, the inefficient routeing decision and complex queueing management of back‐pressure routeing make it unsuitable for practical applications. This study proposes an improved back‐pressure routeing algorithm with one first‐input–first‐output (FIFO) queueing structure using the shortest‐path decision. By making use of the shortest‐path knowledge, the feasible routes quickly converge to the shortest path when the network is lightly loaded. On the other hand, when the network load is heavy, the proposed algorithm remains optimal for exploring all the feasible paths between each source and destination. The back‐pressure routeing design based on a single‐FIFO queue architecture greatly simplifies the complexity of packet queueing management. The authors’ results indicate that the proposed routeing algorithm achieves lower end‐to‐end delay than that of some other back‐pressure algorithms without reducing the network throughput performance.