This work presents a method for volumetric seismic data compression by coupling a 3-D convolution-based autoencoder to a generative adversarial network (GAN). The main challenge of 3-D convolutional autoencoders for data compression is how to fully exploit volumetric redundancy while keeping reasonable latent representation dimensions. Our method is based on a convolutional neural network for seismic data compression called 3DSC. Its encoder and decoder use 3-D convolutions and are connected by a latent representation with the same dimensions as its 2-D network counterparts. Our main hypothesis is that the 3DSC architecture can be improved by adversarial training. We, thus, propose a new 3-D-based seismic data compression method (3DSC-GAN) by coupling the 3DSC network to a GAN. The seismic data decoder is used as a generator of poststack data that are integrated with a discriminator module to better exploit 3-D redundancy. Results show that our method outperforms previous seismic data compression methods for very low target bit rates, increasing the peak signal-to-noise ratio (PSNR) with fairly high visual quality.