Recent research has shown that Large Language Models (LLMs) are vulnerable to automated jailbreak attacks, where adversarial suffixes crafted by algorithms appended to harmful queries bypass safety alignment and trigger unintended responses. Current methods for generating these suffixes are computationally expensive and have low Attack Success Rates (ASR), especially against well-aligned models like Llama2 and Llama3. To overcome these limitations, we introduce **ADV-LLM**, an iterative self-tuning process that crafts adversarial LLMs with enhanced jailbreak ability. Our framework significantly reduces the computational cost of generating adversarial suffixes while achieving nearly 100% ASR on various open-source LLMs. Moreover, it exhibits strong attack transferability to closed-source models, achieving 99% ASR on GPT-3.5 and 49% ASR on GPT-4, despite being optimized solely on Llama3. Beyond improving jailbreak ability, ADV-LLM provides valuable insights for future safety alignment research through its ability to generate large datasets for studying LLM safety.