The invention relates to an exhaust gas control apparatus and a control method for controlling supply of a cleaning agnent. On one aspect, the invention provides the exhaust gas control apparatus. The exhaust gas control apparatus comprises an exhaust gas control component which is arranged in an exhaust system and which control exhaust through removing predetermined component contained in the exhaust, a cleaning agnent supply device which supplies the cleaning agent to the upstream side of the exhaust gas control component and which enables the cleaning agent to be attached to the exhaust gas control component and enables the cleaning agent to react with the predetermined component in the exhaust passing through the exhaust gas control component, and a control device which obtains a cleaning agnet adsorption amount distribution on the exhaust gas control component and controls the supply of the cleaning agent supplied by the cleaning agent supply device based on the cleaning agnet adsorption amount distribution. In a model which obtains in a manner that the exhaust gas control component is divded into a plurality of units in the exhaust flow direction, and the control device obtains the cleaning agnet adsorption amount distribution on the exhaust gas control component based on detection values of cleaning agnet adsorption amounts in the units and/or estimated values.