In cognitive radio networks, compressive sensing has the potential to allow a secondary user to efficiently monitor a wideband spectrum at a sub-Nyquist sampling rate without complex hardware. In general, compressive sensing techniques leverage the assumption of sparsity of the wideband spectrum to recover the spectrum by solving a set of ill-posed linear equations. In this paper, we adopt the framework of a generative adversarial neural network (GAN) in deep learning and propose a deep compressive spectrum sensing GAN (DCSS-GAN), where two neural networks are trained to compete with each other to recover the spectrum from undersampled samples in the time domain. The proposed DCSS-GAN is a data-driven learning approach that does not require a priori statistics about the radio environment. In addition, it is an end-to-end algorithm that directly recovers the information of spectrum occupancy from raw samples and without the need of energy detection. Various simulations show that the proposed DCSS-GAN has a 12.3 to 16.2 performance gain on prediction accuracy at a 1/8th compression ratio compared to the conventional LASSO approach.