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In astronomical observatory projects, raw images are processed so that information about the celestial objects in the images is extracted into catalogs. As such, this source extraction is the basis for the various analysis tasks that are subsequently performed on the catalog products. With the rapid progress of new, large astronomical projects, observational images will be produced every few seconds. This high speed of image production requires fast source extraction. Unfortunately, current source extraction tools cannot meet the speed requirement. To address this problem, we propose to use the GPU (Graphics Processing Unit) to accelerate source extraction. Specifically, we start from SExtractor, an astronomical source extraction tool widely used in astronomy projects, and study its parallelization on the GPU. We identify the object detection and deblending components as the most complex and time-consuming, and design a parallel connected component labelling algorithm for detection and a parallel object tree pruning method for deblending respectively on the GPU. We further parallelize other components, including cleaning, background subtraction, and measurement, effectively on the GPU, such that the entire source extraction is done on the GPU. We have evaluated our GPU-SExtractor in comparison with the original SExtractor on a desktop with an Intel i7 CPU and an NVIDIA GTX670 GPU on a set of real-world and synthetic astronomical images of different sizes. Our results show that the GPU-SExtractor outperforms the original SExtractor by a factor of 6, taking a merely 1.9 second to process a typical 4KX4K image containing 167 thousands objects.