Because the linear motor feeding system always runs in complex working conditions for a long time, its performance and state transition have great randomness. Therefore, abnormal detection is particularly significant for predictive maintenance to promptly discover the running state degradation trend. Aiming at the problem that the abnormal samples of linear motor feed system are few and the samples have time-series features, a method of abnormal operation state detection of a linear motor feed system based on normal sample training was proposed, named GANomaly-LSTM. The method constructs an encoding-decoding-reconstructed encoding network model. Firstly, the time-series features of vibration, current and composite data samples are extracted by the long short-term memory (LSTM) network; Secondly, the three-layer fully connected layer is employed to extract potential feature vectors; Finally, anomaly detection of the system is completed by comparing the potential feature vectors of the two encodings. An experimental platform of the X-Y two-axis linkage linear motor feeding system is built to verify the rationality of the proposed method. Compared with other classical methods such as GANomaly and GAN-AE, the average AUROC index of this method is improved by 17.5% and 9.3%, the average accuracy is enhanced by 11.6% and 15.5%, and the detection time is shortened by 223 ms and 284 ms, respectively. GANomaly-LSTM has successfully proved its superiority for abnormal detection for running state of linear motor feeding systems.