An exhaust gas control apparatus comprising: an adding valve configured to supply a reducing agent into an exhaust pipe of an internal combustion engine; a NOx reduction catalyst configured to remove NOx by the reducing agent being supplied from the adding valve, the NOx reduction catalyst being disposed on an exhaust downstream side of the adding valve in the exhaust pipe; a control device comprising an instantaneous value calculation unit configured to calculate a target instantaneous supply amount based on an engine operation state, the target instantaneous supply amount being a reducing agent supply amount for cooling the adding valve; and the control device further comprising a control unit configured to execute an operation control for the adding valve by using a target cooling supply amount (TQc) as an amount obtained by a part of a difference between a previous target cooling supply amount (TQc[i]) and the target instantaneous supply amount, said part being added to the previous target cooling supply amount, the target cooling supply amount being a target reducing agent supply amount for the cooling of the adding valve, the previous target cooling supply amount being the target cooling supply amount calculated during a previous calculation, the exhaust gas control apparatus being characterized in that the control unit is configured to execute the operation control for the adding valve by using the target instantaneous supply amount as the target cooling supply amount when a temperature as an index of a temperature of the adding valve is equal to or higher than a predetermined temperature and when the previous target cooling supply (TQc[i]) amount is "0". an adding valve configured to supply a reducing agent into an exhaust pipe of an internal combustion engine; a NOx reduction catalyst configured to remove NOx by the reducing agent being supplied from the adding valve, the NOx reduction catalyst being disposed on an exhaust downstream side of the adding valve in the exhaust pipe; a control device comprising an instantaneous value calculation unit configured to calculate a target instantaneous supply amount based on an engine operation state, the target instantaneous supply amount being a reducing agent supply amount for cooling the adding valve; and the control device further comprising a control unit configured to execute an operation control for the adding valve by using a target cooling supply amount (TQc) as an amount obtained by a part of a difference between a previous target cooling supply amount (TQc[i]) and the target instantaneous supply amount, said part being added to the previous target cooling supply amount, the target cooling supply amount being a target reducing agent supply amount for the cooling of the adding valve, the previous target cooling supply amount being the target cooling supply amount calculated during a previous calculation, the exhaust gas control apparatus being characterized in that the control unit is configured to execute the operation control for the adding valve by using the target instantaneous supply amount as the target cooling supply amount when a temperature as an index of a temperature of the adding valve is equal to or higher than a predetermined temperature and when the previous target cooling supply (TQc[i]) amount is "0".