This paper presents a stereo matching algorithm utilizing vertical disparity (SMAVD) in solving the matching problem of stereo vision. SMAVD adopts a two-dimensional Hopfield neural network (HNN) to match the stereo pairs according to the energy function developed to describe three constraints including uniqueness, similarity and compatibility. The similarity of one matched pair is measured according to the difference of its neighboring pixels. The compatibility between two matched pairs is determined from not only smoothness and geometric comparisons but also vertical disparity comparison to improve the matching accuracy. Moreover, SMAVD uses a genetic algorithm to design the parameters of the nonlinear functions employed in the similarity and compatibility measures. By applying the updating rule, the HNN could obtain the correct matched pairs satisfying the constraints. The experimental results on the image pairs acquired from a binocular robot demonstrate that SMAVD could achieve high correct matching percentage with less computation time.