This paper proposes a Graphics Processing Unit (GPU) implementation of the stereo correspondence matching using Phase-Only Correlation (POC). The use of high-accuracy stereo correspondence matching based on POC makes it possible to measure accurate 3D shape of the object using stereo vision, while the drawback of POC-based approach is its high computational cost. Addressing this problem, we propose a GPU implementation of POC-based correspondence matching. Through a set of experiments using a variety of GPUs, we demonstrate that the proposed implementation is high-speed and high-efficiency compared with the CPU implementation. We also apply the proposed approach to a real-time 3D measurement system.