Forcing the answer of the Question Answering (QA) task to be a single text span might be restrictive since the answer can be multiple spans in the context. Moreover, we found that multi-span answers often appear with two characteristics when building the QA system for a real-world application. First, multi-span answers might be caused by users lacking domain knowledge and asking ambiguous questions, which makes the question need to be answered with conditions. Second, there might be hierarchical relations among multiple answer spans. Some recent span-extraction QA datasets include multi-span samples, but they only contain unconditional and parallel answers, which cannot be used to tackle this problem. To bridge the gap, we propose a new task: conditional question answering with hierarchical multi-span answers, where both the hierarchical relations and the conditions need to be extracted. Correspondingly, we introduce CMQA, a Conditional Multiple-span Chinese Question Answering dataset to study the new proposed task. The final release of CMQA consists of 7,861 QA pairs and 113,089 labels, where all samples contain multi-span answers, 50.4% of samples are conditional, and 56.6% of samples are hierarchical. CMQA can serve as a benchmark to study the new proposed task and help study building QA systems for real-world applications. The low performance of models drawn from related literature shows that the new proposed task is challenging for the community to solve.