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Accurate tumor segmentation in PET is crucial in many oncology applications. We developed an adaptive region-growing (ARG) algorithm with a maximum curvature strategy (ARG_MC) for tumor segmentation in PET. The ARG_MC repeatedly applied a confidence connected region-growing algorithm with increasing relaxing factor f. The optimal relaxing factor (ORF) was then determined at the transition point on the f-volume curve, where the volume just grew from the tumor into the surrounding normal tissues. The ARG_MC along with five widely used algorithms were tested on a phantom with 6 spheres at different signal to background ratios and on two clinic datasets including 20 patients with esophageal cancer and 11 patients with non-Hodgkin lymphoma (NHL). The ARG_MC did not require any phantom calibration or any a priori knowledge of the tumor or PET scanner. The identified ORF varied with tumor types (mean ORF  =  9.61, 3.78 and 2.55 respectively for the phantom, esophageal cancer, and NHL datasets), and varied from one tumor to another. For the phantom, the ARG_MC ranked the second in segmentation accuracy with an average Dice similarity index (DSI) of 0.86, only slightly worse than Daisne's adaptive thresholding method (DSI  =  0.87), which required phantom calibration. For both the esophageal cancer dataset and the NHL dataset, the ARG_MC had the highest accuracy with an average DSI of 0.87 and 0.84, respectively. The ARG_MC was robust to parameter settings and region of interest selection, and it did not depend on scanners, imaging protocols, or tumor types. Furthermore, the ARG_MC made no assumption about the tumor size or tumor uptake distribution, making it suitable for segmenting tumors with heterogeneous FDG uptake. In conclusion, the ARG_MC was accurate, robust and easy to use, it provides a highly potential tool for PET tumor segmentation in clinic.