Extremely large image generators offer significant transformative potential across diverse sectors. It allows users to design specific prompts to generate realistic images through some black-box APIs. However, some studies reveal that image generators are notably susceptible to attacks and generate Not Suitable For Work (NSFW) contents by manually designed toxin texts, especially imperceptible to human observers. We urgently need a multitude of universal and transferable prompts to improve the safety of image generators, especially black-box-released APIs. Nevertheless, they are constrained by labor-intensive design processes and heavily reliant on the quality of the given instructions. To achieve this, we introduce a black-box stealthy prompt attack (BSPA) that adopts a retriever to simulate attacks from API users. It can effectively harness filter scores to tune the retrieval space of sensitive words for matching the input prompts, thereby crafting stealthy prompts tailored for image generators. Significantly, this approach is model-agnostic and requires no internal access to the model's features, ensuring its applicability to a wide range of image generators. Building on BSPA, we have constructed an automated prompt tool and a comprehensive prompt attack dataset (NSFWeval). Extensive experiments demonstrate that BSPA effectively explores the security vulnerabilities in a variety of state-of-the-art available black-box models, including Stable Diffusion XL, Midjourney, and DALL-E 2/3. Furthermore, we develop a resilient text filter and offer targeted recommendations to ensure the security of image generators against prompt attacks in the future.