Due to the instability of the hyperspectral imaging system and the atmospheric interference, hyperspectral images (HSIs) often suffer from losing the image information of areas with different shapes, which significantly degrades the data quality and further limits the effectiveness of methods for subsequent tasks. Although mainstream deep learning-based methods have achieved promising inpainting performance, the complicated ground object distributions increase the difficulty of HSIs inpainting in practice. In addition, spectral redundancy and complex texture details are two main challenges for deep neural network-based inpainting methods. To address the above issues, we propose a novel inpainting model based on generative adversarial networks for HSI (HSI-IPGAN). To reduce the redundancy of spectral information, a multi-frequency channel attention module is designed to strengthen the essential channels and suppress the less significant ones, which calculates adaptive weight coefficients by converting feature maps to the frequency domain. Furthermore, we propose to constrain the generation of missing areas from both global and local perspectives, by fully leveraging the HSI texture information, so that the overall structure information and regional texture consistency of the original HSI can be maintained. The proposed method has been extensivelyevaluated on the Indian Pines and FCH datasets. The promising results indicate that HSI-IPGAN outperforms the state-of-the-art methods in quantitative and qualitative assessments.