Cerebral radionecrosis is a significant side effect in radiotherapy for brain cancer. The purpose of this study is to calculate the relative biological effectiveness (RBE) of carbon-ion beams on brain cells and to show RBE-weighted dose distributions for cerebral radionecrosis speculation in a carbon-ion treatment planning system. The RBE value of the radionecrosis for the carbon-ion beam is calculated by the modified microdosimetric kinetic model on the assumption of a typical clinical α/β ratio of 2 Gy for cerebral radionecrosis in X-rays. This calculation method for the RBE-weighted dose is built into the treatment planning system for the carbon-ion radiotherapy. The RBE-weighted dose distributions are calculated on computed tomography (CT) images of four patients who had been treated by carbon-ion radiotherapy for astrocytoma (WHO grade 2) and who suffered from necrosis around the target areas. The necrotic areas were detected by brain scans via magnetic resonance imaging (MRI) after the treatment irradiation. The detected necrotic areas are easily found near high RBE-weighted dose regions. The visual comparison between the RBE-weighted dose distribution and the necrosis region indicates that the RBE-weighted dose distribution will be helpful information for the prediction of radionecrosis areas after carbon-ion radiotherapy.