An exhaust gas control apparatus of an internal combustion engine, the exhaust gas control apparatus comprising: a particulate filter configured to trap particulate matter in exhaust gas that is discharged from the internal combustion engine, the particulate filter being configured to be arranged inside an exhaust passage of the internal combustion engine; and an electronic control unit configured to: i) calculate an estimated trapped amount based on an operating state of the internal combustion engine or a differential pressure before and after the particulate filter, the estimated trapped amount being an estimated value of an amount of the particulate matter, and the particulate matter being trapped in the particulate filter, ii) perform reference temperature increase control that increases a temperature of the particulate filter based on a predetermined reference state in order to remove the particulate matter trapped in the particulate filter, iii) detect an actual temperature that is the temperature of the particulate filter while the reference temperature increase control is being performed, iv) store, in advance, a reference temperature that is the temperature of the particulate filter when it is assumed that the reference temperature increase control has been performed when the amount of the particulate matter trapped in the particulate filter is a predetermined reference initial trapped amount, v) correct the estimated trapped amount based on the actual temperature and the reference temperature, and vi) perform particulate matter removal control that removes the particulate matter from the particulate filter, when the estimated trapped amount exceeds a predetermined upper limit amount. a particulate filter configured to trap particulate matter in exhaust gas that is discharged from the internal combustion engine, the particulate filter being configured to be arranged inside an exhaust passage of the internal combustion engine; and an electronic control unit configured to: i) calculate an estimated trapped amount based on an operating state of the internal combustion engine or a differential pressure before and after the particulate filter, the estimated trapped amount being an estimated value of an amount of the particulate matter, and the particulate matter being trapped in the particulate filter, ii) perform reference temperature increase control that increases a temperature of the particulate filter based on a predetermined reference state in order to remove the particulate matter trapped in the particulate filter, iii) detect an actual temperature that is the temperature of the particulate filter while the reference temperature increase control is being performed, iv) store, in advance, a reference temperature that is the temperature of the particulate filter when it is assumed that the reference temperature increase control has been performed when the amount of the particulate matter trapped in the particulate filter is a predetermined reference initial trapped amount, v) correct the estimated trapped amount based on the actual temperature and the reference temperature, and vi) perform particulate matter removal control that removes the particulate matter from the particulate filter, when the estimated trapped amount exceeds a predetermined upper limit amount. i) calculate an estimated trapped amount based on an operating state of the internal combustion engine or a differential pressure before and after the particulate filter, the estimated trapped amount being an estimated value of an amount of the particulate matter, and the particulate matter being trapped in the particulate filter, ii) perform reference temperature increase control that increases a temperature of the particulate filter based on a predetermined reference state in order to remove the particulate matter trapped in the particulate filter, iii) detect an actual temperature that is the temperature of the particulate filter while the reference temperature increase control is being performed, iv) store, in advance, a reference temperature that is the temperature of the particulate filter when it is assumed that the reference temperature increase control has been performed when the amount of the particulate matter trapped in the particulate filter is a predetermined reference initial trapped amount, v) correct the estimated trapped amount based on the actual temperature and the reference temperature, and vi) perform particulate matter removal control that removes the particulate matter from the particulate filter, when the estimated trapped amount exceeds a predetermined upper limit amount.