Accurate 4D trajectory prediction plays an important role in the sustainable management of future air traffic. Aiming at the problems of inadequate feature utilization, unbalanced overall prediction (OP) result, and weak real-time response in 4D trajectory prediction by machine learning, a fractal dimension feature-prediction (FDFP) model is proposed, starting from the airborne quick access recorder (QAR) trajectory data. Firstly, the trajectory features are classified and transformed according to the aircraft operation characteristics. Then, the long short-term memory (LSTM) network is used to construct the prediction model by fractional dimensions; based on the fractal dimension feature (FDF), the different combinations of influencing factors are selected as the feature matrix, and the optimal prediction model of each dimension is obtained. Finally, 671 city pair trajectory data are used to conduct simulation experiments to verify the accuracy and effectiveness of the model. The experimental results show that the FDFP model performs well, with the mean absolute error (MAE) of longitude and latitude both less than 0.0015°, and the MAE of altitude less than 3 m. Compared with the OP model, the MAE of the FDFP model in these three dimensions decreased by 92%, 81% and 79%, respectively. Compared with experiments without feature transformation, the MAE of the FDFP model is reduced by 75%, 82%, and 69%, respectively. Each prediction of the model takes about 30 ms, which satisfies the real-time prediction conditions and can provide a reference for air traffic operation assessment.