Hyperspectral imagery (HSI) with high spectral resolution contributes to better material discrimination, while the spatial resolution limited by the sensor technique prevents it from accurately distinguishing and analyzing targets. Though generative adversarial network-based HSI super-resolution methods have achieved remarkable progress, the problems of treating vital and unessential features equally in feature expression and training instability still exist. To address these issues, an attention-enhanced generative adversarial network (AEGAN) for HSI spatial super-resolution is proposed, which elaborately designs the enhanced spatial attention module (ESAM) and refined spectral attention module (RSAM) in the attention-enhanced generator. Specifically, the devised ESAM equipped with residual spatial attention blocks (RSABs) facilitates the generator that is more focused on the spatial parts of HSI that are difficult to produce and recover, and RSAM with spectral attention refines spectral interdependencies and guarantees the spectral consistency at the respective pixel positions. Additionally, an especial U-Net discriminator with spectral normalization is enclosed to pay more attention to the detailed informations of HSI and yield to stabilize the training. For producing more realistic and detailed super-resolved HSIs, an attention-enhanced generative loss is constructed to train and constrain the AEGAN model and investigate the high correlation of spatial context and spectral information in HSI. Moreover, to better simulate the complicated and authentic degradation, pseudo-real data are also generated with a high-order degradation model to train the overall network. Experiments on three benchmark HSI datasets illustrate the superior performance of the proposed AEGAN method in HSI spatial super-resolution over the compared methods.