The large-scale self-organizing networks (LSNs) for new power systems are the multi-mode mesh networks combining high speed power line communication and radio-frequency communication (HPLC/RF), which are a promising means to solve the “last mile” problem of ubiquitous access. Due to the complex network topology and communication environment, and rapid service iteration, it is challenging to improve transmission efficiency. In this paper, we proposed the routing and resource allocation algorithms based on graph attention network (GAT) and model for new power systems. First, according to historical data such as delay, reliability, SINR, load ratio, betweenness centrality and level, GAT can calculate different probabilities for nodes with higher level than the central node and select the optimal next hop with the largest probability. This process is executed multiple times on different central nodes to get the best end-to-end path. Secondly, considering the wired and wireless channel interference, packets priority and quality of service (QoS) comprehensively, a dynamic resource allocation model based on the optimal next hop generated by GAT is established, which is aimed to maximize the number of successfully transmitted packets between node pairs. And then a packet priority-based resource allocation algorithm is presented for LSNs for new power systems. Simulation results show that the proposed routing and resource allocation algorithms outperform baselines in terms of throughput, end-to-end delay, hop count and network reliability.