Abnormal behavior detection in crowded scenes has drawn extensive interests in computer vision community due to its various applications, e.g., video surveillance, video analytics, and action recognition. However, it is still a challenging task due to the large-scale variation, perspective distortion, and labeling biases. In this paper, an abnormal crowd behavior detection method based on streak flow and convolutional neural network (SFCNN-ABD) is proposed to address this problem. The SFCNN-ABD learns salient spatial features via a convolutional neural network (CNN) and temporal features with the aid of streak flow and CNN. The SFCNN-ABD consists of two stream CNNs, in which the backbone network is composed of two deep residual networks which are spatial network and temporal network respectively. The spatial network utilizes the raw video frames to extract the appearance features of crowded scenes, whereas the temporal network uses the streak flow to extract the kinematic features. The streak flow can accurately recognize the spatial and temporal changes in the scene, and thus can further boost the proposed the performance. Finally, the outputs of these two networks are fused to detect the abnormal crowd behavior. Experimental results on UMN and VIF benchmark datasets indicate that the proposed method outperforms several state-of-the-art methods and thus illustrates the efficiency of the proposed method.