Accurate trajectory prediction plays a vital role in the sustainable management of future air traffic. To enhance the accuracy of long-term trajectory prediction, a multi-step trajectory prediction method considering regulatory rules was proposed based on airborne quick access recorder (QAR) trajectory data. Firstly, trajectory features were classified and transformed according to the aircraft's operational characteristics. Then, different combinations of influencing factors were selected as the feature matrix based on the fractal dimension feature, and phased sampling was proposed considering the actual air traffic management rules. Finally, a long short-term memory (LSTM) neural network was employed to establish a trajectory prediction model to explore the relationship between aircraft position changes and preceding trajectory point data features. 671 urban-pair trajectory data was used for simulation experiments, and the advantages of the proposed model in terms of effectiveness, robustness, and portability were verified through result analysis and generalization analysis. The research results provide a valuable reference for air traffic management work.