Hyperspectral (HS) pansharpening is of great importance in improving the spatial resolution of HS images for remote sensing tasks. HS image comprises abundant spectral contents, whereas panchromatic (PAN) image provides spatial information. HS pansharpening constitutes the possibility for providing the pansharpened image with both high spatial and spectral resolution. This article develops a specific pansharpening framework based on a generative dual-adversarial network (called PS-GDANet). Specifically, the pansharpening problem is formulated as a dual task that can be solved by a generative adversarial network (GAN) with two discriminators. The spatial discriminator forces the intensity component of the pansharpened image to be as consistent as possible with the PAN image, and the spectral discriminator helps to preserve spectral information of the original HS image. Instead of designing a deep network, PS-GDANet extends GANs to two discriminators and provides a high-resolution pansharpened image in a fraction of iterations. The experimental results demonstrate that PS-GDANet outperforms several widely accepted state-of-the-art pansharpening methods in terms of qualitative and quantitative assessment.