Knowledge Editing-Efficiently modifying the knowledge in large language models has gathered great attention. Current benchmarks primarily use multi-hop question answering to assess and analyze newly injected or updated knowledge. However, we argue that these benchmarks fail to effectively evaluate how well the updated models apply this knowledge in real-life scenarios, particularly when questions require complex reasoning involving one-to-many relationships or multi-step logical intersections. To fill in this gap, we introduce a new benchmark, COMPKE: Complex Question Answering under Knowledge Editing, which includes 11,924 complex questions that reflect real-life situations. We perform a comprehensive evaluation of four different knowledge editing methods in COMPKE, and our results show that the performance of these methods varies between different models. For example, MeLLo achieves an accuracy of 39.47 on GPT-4o-mini but drops significantly to 3.83 on Qwen2.5-3B. We further analyze the reasons behind these results from both methodological and model perspectives. Our dataset will be publicly available on GitHub.