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Federated learning learns a neural network model by aggregating the knowledge from a group of distributed clients under the privacy-preserving constraint. In this work, we show that this paradigm might inherit the adversarial vulnerability of the centralized neural network, i.e., it has deteriorated performance on adversarial examples when the model is deployed. This is even more alarming when federated learning paradigm is designed to approximate the updating behavior of a centralized neural network. To solve this problem, we propose an adversarially robust federated learning framework, named Fed_BVA, with improved server and client update mechanisms. This is motivated by our observation that the generalization error in federated learning can be naturally decomposed into the bias and variance triggered by multiple clients' predictions. Thus, we propose to generate the adversarial examples via maximizing the bias and variance during server update, and learn the adversarially robust model updates with those examples during client update. As a result, an adversarially robust neural network can be aggregated from these improved local clients' model updates. The experiments are conducted on multiple benchmark data sets using several prevalent neural network models, and the empirical results show that our framework is robust against white-box and black-box adversarial corruptions under both IID and non-IID settings.