Recently, Large Language Models (LLMs) have garnered significant attention for their exceptional natural language processing capabilities. However, concerns about their trustworthiness remain unresolved, particularly in addressing "jailbreaking" attacks on aligned LLMs. Previous research predominantly relies on scenarios with white-box LLMs or specific and fixed prompt templates, which are often impractical and lack broad applicability. In this paper, we introduce a straightforward and novel method, named ObscurePrompt, for jailbreaking LLMs, inspired by the observed fragile alignments in Out-of-Distribution (OOD) data. Specifically, we first formulate the decision boundary in the jailbreaking process and then explore how obscure text affects LLM's ethical decision boundary. ObscurePrompt starts with constructing a base prompt that integrates well-known jailbreaking techniques. Powerful LLMs are then utilized to obscure the original prompt through iterative transformations, aiming to bolster the attack's robustness. Comprehensive experiments show that our approach substantially improves upon previous methods in terms of attack effectiveness, maintaining efficacy against two prevalent defense mechanisms. We believe that our work can offer fresh insights for future research on enhancing LLM alignment.