The global stereo matching algorithms are of high accuracy for the estimation of disparity map, but the time-consuming in the optimization process still faces a curse, especially for the image pairs with high resolution and large baseline setting. To improve the computational efficiency of the global algorithms, a disparity range estimation scheme for the global stereo matching is proposed to estimate the disparity map of rectified stereo images in this paper. The projective geometry in a parallel binocular stereo vision is investigated to reveal a relationship between two disparities at each pixel in the rectified stereo images with different baselines, which can be used to quickly obtain a predicted disparity map in a long baseline setting estimated by that in the small one. Then, the drastically reduced disparity ranges at each pixel under a long baseline setting can be determined by the predicted disparity map. Furthermore, the disparity range estimation scheme is introduced into the graph cuts with expansion moves to estimate the precise disparity map, which can greatly save the cost of computing without loss of accuracy in the stereo matching, especially for the dense global stereo matching, compared to the traditional algorithm. Experimental results with the Middlebury stereo datasets are presented to demonstrate the validity and efficiency of the proposed algorithm.