Model Predictive Control (MPC) has been widely applied to the motion planning of autonomous vehicles. An MPC-controlled vehicle is required to predict its own trajectories in a finite prediction horizon according to its model. Beyond this, the vehicle should also incorporate the prediction of the trajectory of its nearby vehicles, or target vehicles (TVs) into its decision-making. The conventional trajectory prediction methods, such as the constant-speed-based ones, are too trivial to accurately capture the potential collision risks. In this report, we propose a novel MPC-based motion planning method for an autonomous vehicle with a set of risk-aware constraints. These constraints incorporate the predicted trajectory of a TV learned using a deep-learning-based method. A recurrent neural network (RNN) is used to predict the TV's future trajectory based on its historical data. Then, the predicted TV trajectory is incorporated into the optimization of the MPC of the ego vehicle to generate collision-free motion. Simulation studies are conducted to showcase the prediction accuracy of the RNN model and the collision-free trajectories generated by the MPC.