Knowledge editing (KE) aims to efficiently and precisely modify the behavior of large language models (LLMs) to update specific knowledge without negatively influencing other knowledge. Current research primarily focuses on white-box LLMs editing, overlooking an important scenario: black-box LLMs editing, where LLMs are accessed through interfaces and only textual output is available. In this paper, we first officially introduce KE on black-box LLMs and then propose a comprehensive evaluation framework to overcome the limitations of existing evaluations that are not applicable to black-box LLMs editing and lack comprehensiveness. To tackle privacy leaks of editing data and style over-editing in current methods, we introduce a novel postEdit framework, resolving privacy concerns through downstream post-processing and maintaining textual style consistency via fine-grained editing to original responses. Experiments and analysis on two benchmarks demonstrate that postEdit outperforms all baselines and achieves strong generalization, especially with huge improvements on style retention (average $+20.82\%\uparrow$).