Stereo matching algorithm based on graph cuts transforms the matching problem to a minimisation of a global energy function, the minimisation can be done by finding out an optimal cut in a special graph. The algorithms has better performance for processing the large low texture areas and the occluded pixels, it is one of the best stereo matching. But Stereo matching algorithm based on graph cuts considers all possible disparities between minimum and maximum values for each pixel, so computation time is very long. In this article, a new method is proposed, only some potential values in the disparity range are selected for each pixel, these values can be found using disparity gradient. This method allows us to make wider disparity range, and at the same time to limit the volume of the graph, and therefore to reduce the computation time. The proposed algorithm is tested with standard stereo images and compared with graph cuts and DP ,experimental results show that proposed algorithm retains the better performance of graph cuts algorithm, and has shorter matching time ,which is 1/25 of original graph cuts algorithm.