In this paper, a long short-term memory (LSTM) neural network model is proposed to replicate simultaneously car-following and lane-changing behaviors in road networks. By combining two kinds of LSTM layers and three input designs of the neural network, six variants of the LSTM model have been created. These models were trained and tested on the NGSIM 101 dataset, and the results were evaluated in terms of longitudinal speed and lateral position respectively. We compared the LSTM model with a classical car- following model (the Intelligent Driving Model (IDM)) in the part of speed decision. In addition, the LSTM model is compared with a model using classical neural networks. LSTM model demonstrates higher accuracy than IDM in car-following behavior and displays better performance regarding both car-following and lane-changing behavior compared to the classical neural network model.