Non-uniform attenuation correction using computed tomography (CT) improves the image quality and quantification of single-photon emission computed tomography (SPECT). However, it is not widely used because it requires a SPECT/CT scanner. This study constructs a convolutional neural network (CNN) to generate attenuation-corrected SPECT images directly from non-attenuation-corrected SPECT images. We constructed an auto-encoder (AE) using a CNN to correct the attenuation in brain perfusion SPECT images. SPECT image datasets of 270 (44,528 slices including augmentation), 60 (5002 slices), and 30 (2558 slices) cases were used for training, validation, and testing, respectively. The acquired projection data were reconstructed in three patterns: uniform attenuation correction using Chang's method (Chang-AC), non-uniform attenuation correction using CT (CT-AC), and no attenuation correction (No-AC). The AE learned an end-to-end mapping between the No-AC and CT-AC images. The No-AC images in the test dataset were loaded into the trained AE, which generated images simulating the CT-AC images as output. The generated SPECT images were employed as attenuation-corrected images using the AE (AE-AC). The accuracy of the AE-AC images was evaluated in terms of the peak signal-to-noise ratio (PSNR) and the structural similarity metric (SSIM). The intensities of the AE-AC and CT-AC images were compared by voxel-by-voxel and region-by-region analysis. The PSNRs of the AE-AC and Chang-AC images, compared using CT-AC images, were 62.2, and 57.9, and their SSIM values were 0.9995 and 0.9985, respectively. The AE-AC and CT-AC images were visually and statistically in good agreement. The proposed AE-AC method yields highly accurate attenuation-corrected brain perfusion SPECT images.