In this paper, we propose an efficient vehicle trajectory prediction framework based on recurrent neural network. Basically, the characteristic of the vehicle’s trajectory is different from that of regular moving objects since it is affected by various latent factors including road structure, traffic rules, and driver’s intention. Previous state of the art approaches use sophisticated vehicle behavior model describing these factors and derive the complex trajectory prediction algorithm, which requires a system designer to conduct intensive model optimization for practical use. Our approach is data-driven and simple to use in that it learns complex behavior of the vehicles from the massive amount of trajectory data through deep neural network model. The proposed trajectory prediction method employs the recurrent neural network called long short-term memory (LSTM) to analyze the temporal behavior and predict the future coordinate of the surrounding vehicles. The proposed scheme feeds the sequence of vehicles’ coordinates obtained from sensor measurements to the LSTM and produces the probabilistic information on the future location of the vehicles over occupancy grid map. The experiments conducted using the data collected from highway driving show that the proposed method can produce reasonably good estimate of future trajectory.