Hyperspectral images (HSIs) always contain abundant spectral and spatial information. Most of the existing deep learning-based hyperspectral anomaly detection methods consider spectral differences between the background and anomalies, and the local spatial information is usually ignored. To make complete use of the spatial–spectral information, this article proposed a local spatial–spectral information-integrated semisupervised two-stream network (LS³T-Net) for hyperspectral anomaly detection. The two-stream network comprises an adaptive convolution and fully connected network and a variational autoencoder (VAE). The adaptive convolution and fully connected network is used to extract the local spatial features of patches, while VAE is trained to learn spectral information close to the background pixels. Furthermore, the detection maps from the two-stream network are incorporated through a process combining the benefits of spatial learning and spectral learning. This enhances the ability to separate the background and anomalies and suppress the false alarm. The experimental results for six real HSI datasets reveal that LS³T-Net can produce more accurate detection results than seven popular benchmark methods.