In this paper, the three-component power decomposition for polarimetric SAR (PolSAR) data with an adaptive volume scattering model is proposed. The volume scattering model is assumed to be reflection-symmetric but parameterized. For each image pixel, the decomposition first starts with determining the adaptive parameter based on matrix similarity metric. Then, a respective scattering power component is retrieved with the established procedure. It has been shown that the proposed method leads to complete elimination of negative powers as the result of the adaptive volume scattering model. Experiments with the PolSAR data from both the NASA/JPL (National Aeronautics and Space Administration/Jet Propulsion Laboratory) Airborne SAR (AIRSAR) and the JAXA (Japan Aerospace Exploration Agency) ALOS-PALSAR also demonstrate that the proposed method not only obtains similar/better results in vegetated areas as compared to the existing Freeman-Durden decomposition but helps to improve discrimination of the urban regions.