Model-based methods can be used to detect anomalies in industrial robots, but they require a high level of expertise and are therefore difficult to implement. The lack of sufficient data on the anomalous operation of industrial robots limits data-driven anomaly detection methods. This study proposes Sliding Window One-Dimensional Convolutional Autoencoder (SW1DCAE), an unsupervised vibration anomaly detection algorithm for industrial robots, that can directly act on the original vibration signal and effectively improve detection accuracy. First, the convolutional neural network and the autoencoder model are effectively integrated to construct a one-dimensional convolutional autoencoder model. Secondly, the sliding window algorithm is used for data enhancement, and the dropout technique is introduced to improve the generalization ability of the model. Finally, the reconstruction error of the input sample is calculated and compared with the error threshold to determine whether the operation state of the industrial robot is normal or not. This study discusses the effect of different convolution kernel widths, sliding window sizes, dropout ratios, and other parameters on model performance. Validation with vibration signals collected from an industrial robot test bench shows that this unsupervised anomaly detection algorithm has good accuracy and F1 score.