In this paper, we have proposed secondary user (SU) resource assignment algorithm for a multi-hop cognitive radio network to improve end-to-end latency. In the multihop networks for spectrum sharing, a traffic-cross, in which multiple flows are crossed each other, degrades the throughput due to appearing high traffic and shortage resource area. However each SU has to protect the flow of primary users (PU). To overcome this problem, we have set the PU acceptable received power which is decided by the acknowledgment (ACK) power from PU receiver to each SU user. From this information, we analyzed the performance of the proposed algorithm to minimize the end-to-end delay of SU multi-hop flow considering PU acceptable interference power by optimizing SU transmit power, where Lagrangian duality based technique has been utilized to solve the optimization problem and effective allocate the power for each SU users.