Traffic speed prediction is a vital part of the intelligent transportation system (ITS). Predicting accurate traffic speed is becoming an important and challenging task with the rapid development of deep learning and increasing traffic data size. In this study, we present a deep-learning-based architecture for network-wide traffic speed prediction. We propose a deep-learning-based model consisting of a fully convolutional neural network, bidirectional long short-term memory, and attention mechanism. Our design aims to consider both backward and forward dependencies of traffic data to predict multistep network-wide traffic speed. Thus, we propose a model named AttBDLTSM-FCN for multistep traffic speed prediction. We augmented the attention-based bidirectional long short-term memory recurrent neural network with the fully convolutional network to predict the network-wide traffic speed. In traffic speed prediction, this is the first time that augmentation of AttBDLSTM and FCN have been exploited to measure the backward dependency of traffic data, as a building block for a deep architecture model. We conducted comprehensive experiments, and the experimental evaluations illustrated that the proposed architecture achieved better performance compared to state-of-the-art models when considering the short and long traffic speed prediction, e.g., 15, 30, and 60 min, in multistep traffic speed prediction.