Recently, the rapid advancements in deep learning within computer vision have unveiled novel pathways for enhancing density analysis in the context of Unmanned Aerial Vehicles (UAVs), catalyzing a proliferation of deep learning-based frameworks for UAV crowd counting. Despite their remarkable performance, nearly all existing approaches are confined to utilizing either CNN or Transformer architectures, overlooking the synergistic advantages that can be harnessed through the integration of diverse learning paradigms. Notably, a groundbreaking learning paradigm known as Mamba has garnered significant attention within the research community. Distinguished by its ability to capture long-term feature dependencies and its linear computational complexity, Mamba represents a promising advancement. Therefore, given the paucity of labeled samples and the inherent limitations of computational resources in UAV counting tasks, this paper proposes a synergistic method, UAVMamba, which amalgamates the strengths of diverse learning paradigms while minimizing computational overhead. UAVMamba consists of four integral components: a locally-focused CNN branch, a globally-focused Mamba branch, and multi-scale supervisory signals, each strategically designed to capture fine-grained features. Extensive experiments conducted on the widely-adopted VisDrone dataset validate that our method outperforms 13 state-of-the-art UAV crowd counting models, thereby underscoring the efficacy of our UAVMamba.