In the analysis of nuclear medicine images, it is generally necessary to recognize organ's boundary and determine some special regions of interest (ROI). This paper will introduce a method of auto-edge detection of the ROI. Due to some spatial properties of nuclear medicine images, traditional method, such as using edge detection operators, sometimes can not give us the correct ROI. The region-growing method is frequently used in image segmentation. Though this method needs a large calculation, it can get exact edge of ROI by utilize several properties of the image directly. So it is adaptive to nuclear medicine image that has small size and a lot of local spatial properties. The procedure of region-growing method is: At first, the image is segmented into several cells. Secondly pick up one typical pixel, examine the value of the pixel with the clinical statistical criterion to decide whether the pixel is a part of the target organ. If it meets the criterion, merge it into the target organ. If not, reject this pixel. Then go on checking all neighbors of the pixel until all image have been examined. By means of the spatial relationship of the pixels, we can easily find the edge of the target organ. Using this method in edge detection of some clinical images such as kidney, heart, liver, we find that the result is better than some other methods.