Real-world data often have an open long-tailed distribution, and building a unified QA model supporting various tasks is vital for practical QA applications. However, it is non-trivial to extend previous QA approaches since they either require access to seen tasks of adequate samples or do not explicitly model samples from unseen tasks. In this paper, we define Open Long-Tailed QA (OLTQA) as learning from long-tailed distributed data and optimizing performance over seen and unseen QA tasks. We propose an OLTQA model that encourages knowledge sharing between head, tail and unseen tasks, and explicitly mines knowledge from a large pre-trained language model (LM). Specifically, we organize our model through a pool of fine-grained components and dynamically combine these components for an input to facilitate knowledge sharing. A retrieve-then-rerank frame is further introduced to select in-context examples, which guild the LM to generate text that express knowledge for QA tasks. Moreover, a two-stage training approach is introduced to pre-train the framework by knowledge distillation (KD) from the LM and then jointly train the frame and a QA model through an adaptive mutual KD method. On a large-scale OLTQA dataset we curate from 43 existing QA datasets, our model consistently outperforms the state-of-the-art. We release the code and data at \url{https://github.com/AlibabaResearch/DAMO-ConvAI/tree/main/oltqa}.
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