In this paper, we propose a new approach for anomaly detection in video surveillance. This approach is based on a nonparametric Bayesian regression model built upon Gaussian process priors. It establishes a set of basic vectors describing motion patterns from low-level features via online clustering, and then constructs a Gaussian process regression model to approximate the distribution of motion patterns in kernel space. We analyze different anomaly measure criterions derived from Gaussian process regression model and compare their performances. To reduce false detections caused by crowd occlusion, we utilize supplement information from previous frames to assist in anomaly detection for current frame. In addition, we address the problem of hyperparameter tuning and discuss the method of efficient calculation to reduce computation overhead. The approach is verified on published anomaly detection datasets and compared with other existing methods. The experiment results demonstrate that it can detect various anomalies efficiently and accurately.