A novel image enhancement method for infrared (IR) images is presented. The proposed method consists of two parts considering the characteristics of high-dynamic-range IR images. First, we attempt to enhance image contrast by introducing the ramp distribution that increases with a constant slope in an ordered histogram domain. The ramp-distributed histogram is incorporated into an optimization problem with a sorted histogram of the input image to calculate a modified histogram. Second, to deal with blurred effects on IR images, we propose a relative edge-strength index for high-boost filtering to effectively suppress noise in relatively uniform regions. Compared with various conventional and state-of-the-art algorithms, the proposed method shows highly competitive performance.