End-to-end delay is an important QoS metric in multihop wireless networks such as sensor networks and mesh networks. Along with throughput, end-to-end delay determines the user-experienced data transmission time. End-to-end delay refers to the total time it takes for a single packet to reach the destination. It is a result of many factors including the length of the route and the interference level along the route, and therefore both the routing scheme and the MAC layer scheduling scheme can affect end-to-end delay. We assume a deterministic scheduling scheme is used at the MAC layer. Since the actual delay depends on the MAC layer scheduling algorithm, at the network layer we try to reduce the interference on the path instead of the actual delay time. To find the routing solution that minimizes path interference, a sufficient condition on conflict-free transmission is established, which helps to quantify the interference on a link. A linear program based on the sufficient condition is developed to compute the routing solution. Through simulation, we show that the proposed routing scheme can effectively reduce end-to-end delay.