Large Language Models (LLMs) have demonstrated remarkable capabilities across a variety of tasks in different domains. However, they sometimes generate responses that are logically coherent but factually incorrect or misleading, which is known as LLM hallucinations. Data-driven supervised methods train hallucination detectors by leveraging the internal states of LLMs, but detectors trained on specific domains often struggle to generalize well to other domains. In this paper, we aim to enhance the cross-domain performance of supervised detectors with only in-domain data. We propose a novel framework, prompt-guided internal states for hallucination detection of LLMs, namely PRISM. By utilizing appropriate prompts to guide changes in the structure related to text truthfulness within the LLM's internal states, we make this structure more salient and consistent across texts from different domains. We integrated our framework with existing hallucination detection methods and conducted experiments on datasets from different domains. The experimental results indicate that our framework significantly enhances the cross-domain generalization of existing hallucination detection methods.