An exhaust after treatment apparatus for an internal combustion engine, comprising: an exhaust after treatment device provided on an exhaust passage; and a fuel supplying device for supplying a fuel component to the exhaust after treatment device, the fuel supplying device being configured to perform a post injection by supplying the fuel component into a cylinder at a timing where fuel does not ignite, the exhaust after treatment apparatus being configured to perform temperature increasing control of the exhaust after treatment device by supplying the fuel component, wherein the exhaust after treatment apparatus further comprises: an exhaust gas temperature detecting device for detecting an exhaust gas temperature in the exhaust passage; an operating state determining unit configured, when given conditions including a condition that the exhaust gas temperature is lower than a given temperature are satisfied, to determine that the internal combustion engine is in an operating state where an active state of the exhaust after treatment device is not maintainable, after supply of a fuel component in a supply amount calculated by a fuel supply amount calculating unit during the temperature increasing control; the fuel supply amount calculating unit configured to calculate the supply amount of the fuel component for the temperature increasing control so that the supply amount becomes larger as the exhaust gas temperature detected by the exhaust gas temperature detecting device becomes lower during the temperature increasing control; a limited fuel supply amount calculating unit configured to calculate and decrease a limited supply amount of the fuel component for the temperature increasing control when the operation state determining unit determines that the internal combustion engine is in the operation condition where active state of the exhaust after treatment device is not maintainable so that the limited supply amount becomes smaller as the exhaust gas temperature detected by the exhaust gas temperature detecting device becomes lower during the temperature increasing control; and a fuel supply amount setting unit for setting a supply amount of the fuel component to be supplied by the fuel supplying device on the basis of the supply amount calculated by the fuel supply amount calculating unit and the limited supply amount calculated by the limited fuel supply amount calculating unit, and wherein the fuel supply amount setting unit is configured to set the supply amount of the fuel component to be supplied to the smaller one between the supply amount calculated by the fuel supply amount calculating unit and the limited supply amount calculated by the limited fuel supply amount calculating unit when the operating state determining unit determines that the internal combustion engine is in the operating state where the active state of the exhaust after treatment device is not maintainable during the temperature increasing control. an exhaust gas temperature detecting device for detecting an exhaust gas temperature in the exhaust passage; an operating state determining unit configured, when given conditions including a condition that the exhaust gas temperature is lower than a given temperature are satisfied, to determine that the internal combustion engine is in an operating state where an active state of the exhaust after treatment device is not maintainable, after supply of a fuel component in a supply amount calculated by a fuel supply amount calculating unit during the temperature increasing control; the fuel supply amount calculating unit configured to calculate the supply amount of the fuel component for the temperature increasing control so that the supply amount becomes larger as the exhaust gas temperature detected by the exhaust gas temperature detecting device becomes lower during the temperature increasing control; a limited fuel supply amount calculating unit configured to calculate and decrease a limited supply amount of the fuel component for the temperature increasing control when the operation state determining unit determines that the internal combustion engine is in the operation condition where active state of the exhaust after treatment device is not maintainable so that the limited supply amount becomes smaller as the exhaust gas temperature detected by the exhaust gas temperature detecting device becomes lower during the temperature increasing control; and a fuel supply amount setting unit for setting a supply amount of the fuel component to be supplied by the fuel supplying device on the basis of the supply amount calculated by the fuel supply amount calculating unit and the limited supply amount calculated by the limited fuel supply amount calculating unit, and wherein the fuel supply amount setting unit is configured to set the supply amount of the fuel component to be supplied to the smaller one between the supply amount calculated by the fuel supply amount calculating unit and the limited supply amount calculated by the limited fuel supply amount calculating unit when the operating state determining unit determines that the internal combustion engine is in the operating state where the active state of the exhaust after treatment device is not maintainable during the temperature increasing control.