4D trajectory prediction is the core element of future air transportation system, which is intended to improve the operational ability and the predictability of air traffic. In this paper, we introduce a novel model to address the short-term trajectory prediction problem in Terminal Manoeuvring Area (TMA) by application of machine learning methods. It consists of two parts: clustering-based preprocessing part and Multi-cells Neural Network (MCNN)-based machine learning part. First, in the preprocessing part, Principle Component Analysis (PCA) is applied to the real 4D trajectory dataset for reducing the vector variable dimensions. Then, the trajectories are clustered into partitions and noises by Density-Based Spatial Clustering of Applications with Noise (DBSCAN) method. After that, the Neural Network (NN) model is chosen as machine learning method to find out the good predicting model for each individual cluster cell. Finally, with the real traffic data in Beijing TMA, the predicted Estimated Time of Arrival (ETA) for each flight is generated. Experiment results demonstrate that our proposed method is effective and robust in the short-term 4D trajectory prediction. In addition, it can make an accurate trajectory prediction in terms of MAE and RMSE with regards to comparative models.