The 4D trajectory is a multi-dimensional time series with plentiful spatial-temporal features and has a high degree of complexity and uncertainty. Aiming at these features of aircraft flight trajectory and the problem that it is difficult for existing trajectory prediction methods to extract spatial-temporal features from the trajectory data at the same time, we propose a novel 4D trajectory prediction hybrid architecture based on deep learning, which combined Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM). An 1D convolution is used to extract the spatial dimension feature of the trajectory, and LSTM is used to mine the temporal dimension feature of the trajectory. Hence the high-precision prediction of the 4D trajectory is realized based on the sufficient fusion of the above features. We use real Automatic Dependent Surveillance -Broadcast (ADS-B) historical trajectory data for experiments and compare the proposed method with a single LSTM model and BP model on the same data set. The experimental results show that the trajectory prediction accuracy of the CNN-LSTM hybrid model is superior to a single model. The prediction error is reduced by an average of 21.62% compared to the LSTM model and by an average of 52.45% compared to the BP model. It provides a certain reference for the trajectory prediction research and Air Traffic Management decision-making.