Multiple unmanned aerial vehicles (Multi-UAV) systems have recently demonstrated significant advantages in some real-world scenarios, but the limited communication range of UAVs poses great challenges to multi-UAV collaborative decision-making. By constructing the multi-UAV cooperation problem as a multi-agent system (MAS), the cooperative decision-making among UAVs can be realized by using multi-agent reinforcement learning (MARL). Following this paradigm, this work focuses on developing partially observable MARL models that capture important information from local observations in order to select effective actions. Previous related studies employ either probability distributions or weighted mean field to update the average actions of neighborhood agents. However, they do not fully consider the feature information of surrounding neighbors, resulting in a local optimum often. In this paper, we propose a novel partially multi-agent reinforcement learning algorithm to remedy this flaw, which is based on graph attention network and partially observable mean field and is named as the GPMF algorithm for short. GPMF uses a graph attention module and a mean field module to describe how an agent is influenced by the actions of other agents at each time step. The graph attention module consists of a graph attention encoder and a differentiable attention mechanism, outputting a dynamic graph to represent the effectiveness of neighborhood agents against central agents. The mean field module approximates the effect of a neighborhood agent on a central agent as the average effect of effective neighborhood agents. Aiming at the typical task scenario of large-scale multi-UAV cooperative roundup, the proposed algorithm is evaluated based on the MAgent framework. Experimental results show that GPMF outperforms baselines including state-of-the-art partially observable mean field reinforcement learning algorithms, providing technical support for large-scale multi-UAV coordination and confrontation tasks in communication-constrained environments.