In order to ensure the safe driving of autonomous vehicles in a human-machine mixed driving environment, the prediction of the cut-in trajectory of surrounding vehicles is of paramount importance. Firstly in this paper, the Savitzky-Golay filter is used for the denoise treatment of large-scale natural driving data collected, the vehicle cut-in fragments are extracted based on criteria, and the vehicle cut-in dataset consistent with the road conditions in China is established. Secondly, by giving play to the advantage of Bi-LSTM in fully utilizing context and the ability of in-out swift connection in effectively reducing gradient disappearance and network degeneration, an improved bi-directional long short-term memory (Bi-LSTM) neural network based on deep learning is proposed to predict the trajectory of cut-in vehicle, and the swift connection is introduced on the basis of Bi-LSTM with comprehensive consideration of the effects of ego vehicle on the cut-in of surrounding vehicles. A test verification is conducted on the natural driving dataset and NGSIM dataset with a result showing that the trajectory prediction effects of the improved Bi-LSTM prediction model proposed are significantly better than other methods, having important significance in enhancing the safety of autonomous vehicles.