Past few years have witnessed vigorous progress in multi-target tracking (MTT) control of unmanned aerial vehicle (UAV) swarm. Most existing target tracking approaches rely on ideally assuming a preset target trajectory. However, in practice, the trajectory of moving target cannot be known by UAV in advance, which brings a great challenge to realize real-time tracking. Meanwhile, state-of-the-art multi-agent value-based methods has achieved significant progress in cooperative tasks. In contrast, multi-agent actor-critic (MAAC) methods do not provide satisfying performance. To address aforementioned issues, this paper proposes factored multi-agent soft actor-critic (FMASAC) scheme, where UAV swarm is enabled to learn cooperative MTT in unknown environment. This method introduces the idea of value decomposition into the MAAC setting to reduce the variance in policy updates and learn efficient credit assignment. Experiments demonstrate that FMASAC significantly improves cooperative MTT performance of UAV swarm, and outperforms the MAAC baselines in terms of the mean return and tracking success rate.