With the aim of handling the characteristics of infrared images, including their high dynamic range (HDR), low contrast, and blurry edges, this paper proposes an approach for displaying infrared images with gradient domain guided image filter (GIF). First, the original image is decomposed into base layer and detail layer by gradient domain GIF and Gaussian filter. Second, the adaptive double plateau histogram equalization method is used to compress the dynamic range and enhance the overall brightness of the base layer. Third, a detail gain factor is constructed to gain the detail layer, and then a display method for the detail layer is designed by considering the 3 sigma rule in Gaussian distributions. Finally, the processed base layer and detail layer are linearly fused to obtain the result image. The proposed method and five mainstream infrared image display methods are used to process infrared images collected in four different scenes. Subjective and objective evaluation methods are used to demonstrate that the proposed method is capable of compressing the dynamic range, improving the overall brightness and enhancing the local details, as well as displaying HDR infrared images with a high degree of fidelity.