Constant false alarm rate (CFAR) detector is a class of widely used methods for target detection in radar images. Classical CFAR detectors perform target detection on a pixel-by-pixel basis using certain sliding windows for estimating clutter statistics, which run fast for small images. However, as the image size gets large, the time cost of these detectors will increase significantly since the time complexity with respect to -pixel image is . In practice, radar images, such as those in synthetic aperture radar (SAR), usually have very large numbers of pixels (which can be on the order of ), making the classical CFAR detectors very time-consuming when applied to these images. In this article, we present graphics processing unit (GPU)-oriented Designs for speeding up CFAR detectors, including smallest/greatest-of CFAR and order-statistic CFAR. The proposed designs implement CFAR detectors via tensor operations, including tensor convolution, shift, and Boolean operation, which can be fast operated by GPU. Experimental results show that the proposed GPU-oriented CFAR detectors running on a high-performance Nvidia RTX 3090 GPU can be thousands of times faster than the classical CFAR detectors, and realize real-time target detection in large-size radar images. Examples using SAR and range-Doppler images are provided as illustrative applications of the proposed GPU CFAR detectors to target detection in radar images.