Local dimming of the LED backlight is a popular technique for saving the power of a liquid crystal display. This paper presents a novel approach that improves the performance of conventional local dimming algorithms by incorporating a visual attention prediction model in the backlight dimming process. The approach saves the energy of the liquid crystal display and, in the mean time, maintains the perceptual image quality. This is achieved by preserving the backlight luminance of the image areas that attract human attention while reducing that of the other image areas. Experimental results are provided to show the effectiveness of the proposed approach.