The hunting motion generated by high-speed trains can seriously affect the safety of trains, so predicting hunting motion can provide early warning. The current research on hunting motion is mainly about the prediction of hunting instability, but there is a small-amplitude hunting intermediate state between normal and hunting instability during train operation, and the prediction of the small-amplitude hunting state can provide early warning of hunting instability. To this end, a prediction method for imbalanced data based on a one-dimensional convolutional neural network 1D-CNN and a conditional generative adversarial network CGAN is proposed for the extreme imbalanced case of high-speed train hunting motion data using the bogie lateral acceleration signal as the standard. The adversarial learning mechanism of CGAN method first utilised to optimise the update parameters through a game between the generator and the discriminator. The well-trained CGAN model is then used to generate samples, feed the enhanced data into a 1D-CNN classifier, and output the prediction results. Experiments are conducted on actual high-speed train operation data, and the results show that CGAN can fit the data distribution of high-speed train hunting fault motion and enhance the dataset, and the prediction accuracy based on the proposed method is 97.5%, which is substantially better than the comparison method. Thus the CGAN-1DCNN-based minor hunting prediction method can predict minor hunting under data imbalance and achieve early warning of hunting instability.