© 2002-2011 IEEE. It has been recognized as a significant issue that the magnetization of RE-123 coated conductors affects the spatial homogeneity and the time variation of the magnetic field of the magnets for MRI, NMR, and accelerators. Therefore, the understanding and the modelling of the magnetization of a coated conductor are crucial for the quantitative estimation and the compensation of its influence on a magnet. On the other hand, the magnetization of the coated conductor has been usually measured and analyzed as a global value; then it is difficult to clarify the local electromagnetic behavior governing such a global performance. Furthermore, such behavior should be investigated under the condition not only with external magnetic field but also with DC transport current as is exposed in a magnet. In this study, the magnetization of a coated conductor was characterized by a spatially-resolved measurement based on the scanning Hall-probe microscopy (SHPM). The magnitude and the time variation of the magnetization were clarified from the visualized magnetization current distribution and its time variation. In particular, they were modeled successfully including the influence of the transport current. Furthermore, taking account of the findings, the experimental results were successfully reconstructed by a numerical analysis based on finite element method (FEM). This will contribute to the quantitative estimation and the compensation of the magnetization problem for the magnets comprising RE-123 coated conductors.