For driving safely and comfortably, the long-term trajectory prediction of surrounding vehicles is essential for autonomous vehicles. For handling the uncertain nature of trajectory prediction, deep-learning-based approaches have been proposed previously. An on-road vehicle must obey road geometry, i.e., it should run within the constraint of the road shape. Herein, we present a novel road-aware trajectory prediction method which leverages the use of high-definition maps with a deep learning network. We developed a data-efficient learning framework for the trajectory prediction network in the curvilinear coordinate system of the road and a lane assignment for the surrounding vehicles. Then, we proposed a novel output-constrained sequence-to-sequence trajectory prediction network to incorporate the structural constraints of the road. Our method uses these structural constraints as prior knowledge for the prediction network. It is not only used as an input to the trajectory prediction network, but is also included in the constrained loss function of the maneuver recognition network. Accordingly, the proposed method can predict a feasible and realistic intention of the driver and trajectory. Our method has been evaluated using a real traffic dataset, and the results thus obtained show that it is data-efficient and can predict reasonable trajectories at merging sections.