In this paper, we propose a new sharpness enhancement algorithm for stereo images. Although the stereo image and its applications are becoming increasingly prevalent, there has been very limited research on specialized image enhancement solutions for stereo images. Recently, a binocular just-noticeable-difference (BJND) model that describes the sensitivity of the human visual system to luminance changes in stereo images has been presented. We introduce a novel application of the BJND model for the sharpness enhancement of stereo images. To this end, an overenhancement problem in the sharpness enhancement of stereo images is newly addressed, and an efficient solution for reducing the overenhancement is proposed. The solution is found within an optimization framework with additional constraint terms to suppress the unnecessary increase in luminance values. In addition, the reliability of the BJND model is taken into account by estimating the accuracy of stereo matching. Experimental results demonstrate that the proposed algorithm can provide sharpness-enhanced stereo images without producing excessive distortion.