With growing dependence of industrial robots, a failure of an industrial robot may interrupt current operation or even overall manufacturing workflows in the entire production line, which can cause significant economic losses. Hence, it is very essential to maintain industrial robots to ensure high-level performance. It is widely desired to have a real-time technique to constantly monitor robots by collecting time series data from robots, which can automatically detect incipient failures before robots totally shut down. Model-based methods are typically used in anomaly detection for robots, yet explicit domain knowledge and accurate mathematical models are required. Data-driven techniques can overcome these limitations. However, a major difficulty for them is the lack of sufficient fault data of industrial robots. Besides, the used technique for anomaly detection of robots should be required to not only capture the temporal dependency in collected time series data, but also the inter-correlations between different metrics. In this paper, we introduce an unsupervised anomaly detection for industrial robots, sliding-window convolutional variational autoencoder (SWCVAE), which can realize real-time anomaly detection spatially and temporally by coping with multivariate time series data. This method has been verified by a KUKA KR6R 900SIXX industrial robot, and the results prove that the proposed model can successfully detect anomaly in the robot. Thus, this work presents a promising tool for condition-based maintenance of industrial robots.