In the field of robotics and automation, navigation systems based on Large Language Models (LLMs) have recently demonstrated impressive performance. However, the security aspects of these systems have received relatively less attention. This paper pioneers the exploration of vulnerabilities in LLM-based navigation models in urban outdoor environments, a critical area given the widespread application of this technology in autonomous driving, logistics, and emergency services. Specifically, we introduce a novel Navigational Prompt Attack that manipulates LLM-based navigation models by perturbing the original navigational prompt, leading to incorrect actions. Based on the method of perturbation, our attacks are divided into two types: Navigational Prompt Insert (NPI) Attack and Navigational Prompt Swap (NPS) Attack. We conducted comprehensive experiments on an LLM-based navigation model that employs various LLMs for reasoning. Our results, derived from the Touchdown and Map2Seq street-view datasets under both few-shot learning and fine-tuning configurations, demonstrate notable performance declines across seven metrics in the face of both white-box and black-box attacks. Moreover, our attacks can be easily extended to other LLM-based navigation models with similarly effective results. These findings highlight the generalizability and transferability of the proposed attack, emphasizing the need for enhanced security in LLM-based navigation systems. As an initial countermeasure, we propose the Navigational Prompt Engineering (NPE) Defense strategy, which concentrates on navigation-relevant keywords to reduce the impact of adversarial attacks. While initial findings indicate that this strategy enhances navigational safety, there remains a critical need for the wider research community to develop stronger defense methods to effectively tackle the real-world challenges faced by these systems.