Contrast enhancement plays a crucial role in infrared image pre-processing. Compared with the increasingly popular local-mapping enhancement methods, the global-mapping enhancement methods have a unique feature that reserves the thermal distribution information, which is vital in some temperature-sensitive applications. However, the main challenge of the global-mapping methods is how to enhance the contrast effectively without suffering from over-enhancement of the background and noise. To this end, we propose a novel global-mapping enhancement algorithm in this paper. First, the histogram is divided into several sub-histograms adaptively based on the heat conduction theory. By designing a metric called AHV, the background and non-background sub-histograms are distinguished, and then enhanced separately where more grayscales are allocated to non-background sub-histograms than background sub-histograms. Meanwhile, the property of the human visual system described by Weber's law is also taken into consideration during the grayscale redistribution. The qualitative and quantitative comparisons with state-of-the-art methods on several databases demonstrate the advantages of our proposed method.