An exhaust gas control apparatus for an internal combustion engine, comprising: an adding mechanism configured to add urea water to exhaust gas of the internal combustion engine; a catalyst configured to adsorb ammonia generated from the urea water, the catalyst being configured to remove NOx by using the ammonia which is adsorbed on the catalyst; and an electronic control unit configured to: set a target adsorption amount of the ammonia adsorbed on the catalyst, the electronic control unit being configured to control the adding mechanism such that the amount of the urea water addition to the exhaust gas is an addition amount calculated based on the target adsorption amount; execute an initialization process for decreasing the amount of the ammonia adsorbed on the catalyst to "0" if an integrated value of the amount of the NOx flowing into the catalyst is equal to or higher than a predetermined value; execute a temperature-raising process for raising a temperature of the exhaust gas flowing into the catalyst as the initialization process; as the temperature-raising process, raise the temperature of the exhaust gas to a temperature at which the ammonia is desorbed from the catalyst; measure a length of time for which the initialization process is executed; and execute the initialization process until the measured length of time for which the initialization process is executed reaches a threshold determined in advance. an adding mechanism configured to add urea water to exhaust gas of the internal combustion engine; a catalyst configured to adsorb ammonia generated from the urea water, the catalyst being configured to remove NOx by using the ammonia which is adsorbed on the catalyst; and an electronic control unit configured to: set a target adsorption amount of the ammonia adsorbed on the catalyst, the electronic control unit being configured to control the adding mechanism such that the amount of the urea water addition to the exhaust gas is an addition amount calculated based on the target adsorption amount; execute an initialization process for decreasing the amount of the ammonia adsorbed on the catalyst to "0" if an integrated value of the amount of the NOx flowing into the catalyst is equal to or higher than a predetermined value; execute a temperature-raising process for raising a temperature of the exhaust gas flowing into the catalyst as the initialization process; as the temperature-raising process, raise the temperature of the exhaust gas to a temperature at which the ammonia is desorbed from the catalyst; measure a length of time for which the initialization process is executed; and execute the initialization process until the measured length of time for which the initialization process is executed reaches a threshold determined in advance. set a target adsorption amount of the ammonia adsorbed on the catalyst, the electronic control unit being configured to control the adding mechanism such that the amount of the urea water addition to the exhaust gas is an addition amount calculated based on the target adsorption amount; execute an initialization process for decreasing the amount of the ammonia adsorbed on the catalyst to "0" if an integrated value of the amount of the NOx flowing into the catalyst is equal to or higher than a predetermined value; execute a temperature-raising process for raising a temperature of the exhaust gas flowing into the catalyst as the initialization process; as the temperature-raising process, raise the temperature of the exhaust gas to a temperature at which the ammonia is desorbed from the catalyst; measure a length of time for which the initialization process is executed; and execute the initialization process until the measured length of time for which the initialization process is executed reaches a threshold determined in advance.