A conventional target detection technique for FMCW millimeter-wave radar applies a two-dimensional (2D) cell-averaging constant false alarm rate (CA-CFAR) detector to all range-Doppler cells in order to suppress noise and clutter. However, this 2D CA-CFAR method has significant drawbacks, particularly its high computational cost due to the large number of additions required, resulting in a time complexity of O(n^{4}). To decrease the computational complexity while ensuring the detection accuracy, a novelty CA-CFAR technique based on the prefix sum algorithm with the complexity O(n^{2}) is proposed in this article. Simulations prove the feasibility of the proposed method. Compared to both conventional and state-of-the-art optimized CA-CFAR techniques, the proposed method reduces the number of addition operations by 95%, lowers CFAR loss by approximately 0.5 dB, and improves the figure of merit (FoM) by about 20% at a fixed false alarm rate of 10^{-6}. This advanced technique offers significant computational efficiency for radar applications.