The rapid variation of wireless channels and feedback delay make the available channel state information (CSI) outdated in dynamic wireless multi-hop networks, which significantly degrades the accuracy of cross-layer resource allocation. To deal with this problem, a cross-layer resource allocation scheme is proposed for wireless multi-hop networks by taking the outdated CSI into account and basing compensation on the results of channel prediction. The cross-layer resource allocation is formulated as a network utility maximization problem, which jointly considers congestion control, channel allocation, power control, scheduling and routing with the compensated CSI. Based on a dual decomposition approach, the problem is solved in a distributed manner. Simulation results show that the proposed algorithm can reasonably allocate the resources, and significantly improve the throughput and energy efficiency in the network.