Abnormal crowd behavior detection has recently attracted increasing attention due to its wide applications in computer vision research areas. However, it is still an extremely challenging task due to the great variability of abnormal behavior coupled with huge ambiguity and uncertainty of video contents. To tackle these challenges, we propose a new probabilistic framework named variational abnormal behavior detection (VABD), which can detect abnormal crowd behavior in video sequences. We make three major contributions: (1) We develop a new probabilistic latent variable model that combines the strengths of the U-Net and conditional variational auto-encoder, which also are the backbone of our model; (2) We propose a motion loss based on an optical flow network to impose the motion consistency of generated video frames and input video frames; (3) We embed a Wasserstein generative adversarial network at the end of the backbone network to enhance the framework performance. VABD can accurately discriminate abnormal video frames from video sequences. Experimental results on UCSD, CUHK Avenue, IITB-Corridor, and ShanghaiTech datasets show that VABD outperforms the state-of-the-art algorithms on abnormal crowd behavior detection. Without data augmentation, our VABD achieves 72.24% in terms of AUC on IITB-Corridor, which surpasses the state-of-the-art methods by nearly 5%.