To effectively extract the temporal information between consecutive video frames， a prediction network IndRNN-VAE （Independently Recurrent Neural Network-Variational AutoEncoder） that fuses Independently Recurrent Neural Network （IndRNN） and Variational AutoEncoder （VAE） network was proposed. Firstly， the spatial information of video frames was extracted through VAE network， and the latent features of video frames were obtained by a linear transformation. Secondly， the latent features were used as the input of IndRNN to obtain the temporal information of the sequence of video frames. Finally， the obtained latent features and temporal information were fused through residual block and input to the decoding network to generate the prediction frame. By testing on UCSD Ped1， UCSD Ped2 and Avenue public datasets， experimental results show that compared with the existing anomaly detection methods， the method based on IndRNN-VAE has the performance significantly improved， and has the Area Under Curve （AUC） values reached 84.3%， 96.2%， and 86.6% respectively， the Equal Error Rate （EER） values reached 22.7%， 8.8%， and 19.0% respectively， the difference values in the mean anomaly scores reached 0.263， 0.497， and 0.293 respectively. Besides， the running speed of this method reaches 28 FPS （Frames Per Socond）.