Despite remarkable successes in solving various complex decision-making tasks, training an imitation learning (IL) algorithm with deep neural networks (DNNs) suffers from the high-computational burden. In this work, we propose quantum IL (QIL) with a hope to utilize quantum advantage to speed up IL. Concretely, we develop two QIL algorithms: quantum behavioral cloning (Q-BC) and quantum generative adversarial IL (Q-GAIL). Q-BC is trained with a negative log-likelihood (NLL) loss in an offline manner that suits extensive expert data cases, whereas Q-GAIL works in an inverse reinforcement learning (IRL) scheme, which is online, on-policy, and is suitable for limited expert data cases. For both QIL algorithms, we adopt variational quantum circuits (VQCs) in place of DNNs for representing policies, which are modified with data reuploading and scaling parameters to enhance the expressivity. We first encode classical data into quantum states as inputs, then perform VQCs, and finally measure quantum outputs to obtain control signals of agents. Experiment results demonstrate that both Q-BC and Q-GAIL can achieve comparable performance compared to classical counterparts, with the potential of quantum speedup. To our knowledge, we are the first to propose the concept of QIL and conduct pilot studies, which paves the way for the quantum era.