In this paper, we propose a secondary user (SU) resource assignment algorithm for a multi-hop (MH) cognitive radio network to improve the end-to-end throughput. In the MH networks used for spectrum sharing, each SU needs to improve the throughput by taking the primary user (PU) protection into account. For overcoming this problem, we estimate the PU acceptable received power, which is determined by the acknowledgment packet (ACK) power from the PU receiver at each SU. With this estimation, we propose an SU optimal transmit power control algorithm to not only maximize the end-to-end throughput of the SU MH flow but also maintain the considered PU acceptable interference power. In this study, a distributed joint allocation algorithm has been used to solve the optimization problem and to effectively allocate the power of each SU.