In multi-turn dialogue, utterances do not always take the full form of sentences. These incomplete utterances will greatly reduce the performance of open-domain dialogue systems. Restoring more incomplete utterances from context could potentially help the systems generate more relevant responses. To facilitate the study of incomplete utterance restoration for open-domain dialogue systems, a large-scale multi-turn dataset Restoration-200K is collected and manually labeled with the explicit relation between an utterance and its context. We also propose a “pick-and-combine” model to restore the incomplete utterance from its context. Experimental results demonstrate that the annotated dataset and the proposed approach significantly boost the response quality of both single-turn and multi-turn dialogue systems.