Traditional methods for plan path prediction have low accuracy and stability. In this paper, we propose a novel approach for plan path prediction based on relative motion between positions (RMBP) by mining historical flight trajectories. A probability statistical model is introduced to model the stochastic factors during the whole flight process. The model object is the sequence of velocity vectors in the three-dimensional Earth space. First, we model the moving trend of aircraft including the speed (constant, acceleration, or deceleration), yaw (left, right, or straight), and pitch (climb, descent, or cruise) using a hidden Markov model (HMM) under the restrictions of aircraft performance parameters. Then, several Gaussian mixture models (GMMs) are used to describe the conditional distribution of each moving trend. Once the models are built, machine learning algorithms are applied to obtain the optimal parameters of the model from the historical training data. After completing the learning process, the velocity vector sequence of the flight is predicted by the proposed model under the Bayesian framework, so that we can use kinematic equations, depending on the moving patterns, to calculate the flight position at every radar acquisition cycle. To obtain higher prediction accuracy, a uniform interpolation method is used to correct the predicted position each second. Finally, a plan trajectory is concatenated by the predicted discrete points. Results of simulations with collected data demonstrate that this approach not only fulfils the goals of traditional methods, such as the prediction of fly-over time and altitude of waypoints along the planned route, but also can be used to plan a complete path for an aircraft with high accuracy. Experiments are conducted to demonstrate the superiority of this approach to some existing methods.