Aerial Vision-and-Language Navigation (VLN) is a novel task enabling Unmanned Aerial Vehicles (UAVs) to navigate in outdoor environments through natural language instructions and visual cues. It remains challenging due to the complex spatial relationships in outdoor aerial scenes. In this paper, we propose an end-to-end zero-shot framework for aerial VLN tasks, where the large language model (LLM) is introduced as our agent for action prediction. Specifically, we develop a novel Semantic-Topo-Metric Representation (STMR) to enhance the spatial reasoning ability of LLMs. This is achieved by extracting and projecting instruction-related semantic masks of landmarks into a top-down map that contains the location information of surrounding landmarks. Further, this map is transformed into a matrix representation with distance metrics as the text prompt to the LLM, for action prediction according to the instruction. Experiments conducted in real and simulation environments have successfully proved the effectiveness and robustness of our method, achieving 15.9% and 12.5% improvements (absolute) in Oracle Success Rate (OSR) on AerialVLN-S dataset.