With the rapid development of large language models (LLM), robots are starting to enjoy the benefits of new interaction methods that large language models bring. Because edge computing fulfills the needs for rapid response, privacy, and network autonomy, we believe it facilitates the extensive deployment of large models for robot navigation across various industries. To enable local deployment of language models on edge devices, we adopt some model boosting methods. In this paper, we propose FASTNav - a method for boosting lightweight LLMs, also known as small language models (SLMs), for robot navigation. The proposed method contains three modules: fine-tuning, teacher-student iteration, and language-based multi-point robot navigation. We train and evaluate models with FASTNav in both simulation and real robots, proving that we can deploy them with low cost, high accuracy and low response time. Compared to other model compression methods, FASTNav shows potential in the local deployment of language models and tends to be a promising solution for language-guided robot navigation on edge devices.