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Activity understanding in visual surveillance has attracted much attention in recent years. In this paper, we present a new method for learning patterns of object activities in image sequences for anomaly detection and activity prediction. The activity patterns are constructed using unsupervised learning of motion trajectories and object features. Based on the learned activity patterns, anomaly detection and activity prediction can be achieved. Unlike existing neural network based methods, our method uses a whole trajectory as an input to the network. This makes the network structure much simpler. Furthermore, the fuzzy set theory based method and the batch learning method are introduced into the network learning process, and make the learning process much more efficient. Two sets of data acquired, respectively, from a model scene and a campus scene are both used to test the proposed algorithms. Experimental results show that the fuzzy self-organizing neural network (fuzzy SOM) is much more efficient than the Kohonen self-organizing feature map (SOFM) and vector quantization in both speed and accuracy, and the anomaly detection and activity prediction algorithms have encouraging performances.