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Hyperspectral anomaly detection (HAD) is an important application of hyperspectral images (HSI) that can distinguish anomalies from background in an unsupervised manner. As a common unsupervised network in deep learning, autoencoders (AE) have been widely used in HAD and can highlight anomalies by reconstructing the background. This study proposed a novel spatial–spectral joint HAD method based on a two-branch 3D convolutional autoencoder and spatial filtering. We used the two-branch 3D convolutional autoencoder to fully extract the spatial–spectral joint features and spectral interband features of HSI. In addition, we used a morphological filter and a total variance curvature filter for spatial detection. Currently, most of the datasets used to validate the performance of HAD methods are airborne HSI, and there are few available satellite-borne HSI. For this reason, we constructed a dataset of satellite-borne HSI based on the GF-5 satellite for experimental validation of our anomaly detection method. The experimental results for the airborne and satellite-borne HSI demonstrated the superior performance of the proposed method compared with six state-of-the-art methods. The area under the curve (AUC) values of our proposed method on different HSI reached above 0.9, which is higher than those of the other methods.