In this study, we propose an efficient stereo matching method which estimates sparse disparities using global phase only correlation (POC). Conventionally, cost functions are to be calculated for all disparity candidates and the associated computational cost has been impediment in achieving a real-time performance. Therefore, we consider to use fullimage 2D phase only correlation (FIPOC) for detecting the valid disparity candidates. This will require comparatively fewer calculations for the same number of disparity. Since the FIPOC output indicates the disparity distribution of two stereo images, we can sort the disparity candidates and choose them for sparse calculation. In our proposed method, the searchable disparity range is half of the input image size, which is much wider than that of the conventional methods. When we applied the FIPOC to naive sum of absolute difference (SAD) stereo matching method, the combined algorithm required fewer calculations while maintaining the same accuracy. In our evaluation, the proposed method achieved 194 disparities stereo matching in 70 ms on 398 x 288 images without the need for SIMD instruction, multi-thread operation, or additional hardware while using the Intel Core i5-5257U.