Foundation model-based agents are increasingly used to automate complex tasks, enhancing efficiency and productivity. However, their access to sensitive resources and autonomous decision-making also introduce significant security risks, where successful attacks could lead to severe consequences. To systematically uncover these vulnerabilities, we propose AdvAgent, a black-box red-teaming framework for attacking web agents. Unlike existing approaches, AdvAgent employs a reinforcement learning-based pipeline to train an adversarial prompter model that optimizes adversarial prompts using feedback from the black-box agent. With careful attack design, these prompts effectively exploit agent weaknesses while maintaining stealthiness and controllability. Extensive evaluations demonstrate that AdvAgent achieves high success rates against state-of-the-art GPT-4-based web agents across diverse web tasks. Furthermore, we find that existing prompt-based defenses provide only limited protection, leaving agents vulnerable to our framework. These findings highlight critical vulnerabilities in current web agents and emphasize the urgent need for stronger defense mechanisms. We release code at https://ai-secure.github.io/AdvAgent/.