Event argument extraction, which aims to identify arguments of specific events and label their roles, is a challenging subtask of event extraction. Previous approaches solve this problem in a twostage manner that first extracts named entities as argument candidates and then determines their roles. However, many nested entities may be missed or wrongly predicted during the argument candidate extraction procedure, which substantially affects the performance of the downstream classifier. In this paper, we propose a novel one-step question answering based framework, which performs argument candidate extraction and argument role classification simultaneously to mitigate the error propagation problem in conventional two-stage methods. Since the conventional question answering based framework cannot be applied directly to this task, we design a Question Answering based Sequence Labeling (QA-SL) model to tackle inexistent argument roles and multiple argument token spans. Moreover, considering the overwhelming number of parameters in question answering based neural network models and the relatively small size of event extraction corpus, we fine-tune the pre-trained model from BERT to mitigate the data scarcity problem. Extensive experiments demonstrate the benefits of the proposed method, leading to a competitive performance compared with state-of-the-art methods. To the best of our knowledge, this is the first work to cast event argument extraction as a question answering task.