Despite rapid advancements in text-to-image (T2I) models, their safety mechanisms are vulnerable to adversarial prompts, which maliciously generate unsafe images. Current red-teaming methods for proactively assessing such vulnerabilities usually require white-box access to T2I models, and rely on inefficient per-prompt optimization, as well as inevitably generate semantically meaningless prompts easily blocked by filters. In this paper, we propose APT (AutoPrompT), a black-box framework that leverages large language models (LLMs) to automatically generate human-readable adversarial suffixes for benign prompts. We first introduce an alternating optimization-finetuning pipeline between adversarial suffix optimization and fine-tuning the LLM utilizing the optimized suffix. Furthermore, we integrates a dual-evasion strategy in optimization phase, enabling the bypass of both perplexity-based filter and blacklist word filter: (1) we constrain the LLM generating human-readable prompts through an auxiliary LLM perplexity scoring, which starkly contrasts with prior token-level gibberish, and (2) we also introduce banned-token penalties to suppress the explicit generation of banned-tokens in blacklist.Extensive experiments demonstrate the excellent red-teaming performance of our human-readable, filter-resistant adversarial prompts, as well as superior zero-shot transferability which enables instant adaptation to unseen prompts and exposes critical vulnerabilities even in commercial APIs (e.g., Leonardo.Ai.).