An apparatus for post-processing exhaust gas for removing sulfur oxides, the apparatus comprising: a catalytic device including a diesel oxidation catalyst and a selective catalytic reduction; an input unit configured to receive one or more elements of operation information of a vehicle among an engine operation time, an engine fuel consumption quantity, a vehicle trip distance, and sulfur oxides produced quantity; a memory unit configured to store a first operation information value for processing sulfur oxides and a second operation information value for processing sulfur oxides, wherein the first operation information value and the second operation information value are generated by evaluating the operation information received from the input unit; a first processing unit configured to determine whether the first operation information value stored in the memory unit reaches a predetermined first reference value, and command a low temperature control when the first operation information value reaches the first reference value; a second processing unit configured to determine whether the second operation information value stored in the memory unit reaches a predetermined second reference value, and command a high temperature control when the second operation information value reaches the predetermined second reference value; characterised by a sulfur oxides removal operating unit configured to remove a first sulfur oxides by heating the catalytic device under a first temperature condition when the low temperature control command is generated from the first processing unit, and remove the first sulfur oxides and a second sulfur oxides which is different from the first sulfur oxides and removed at a higher temperature than the first sulfur oxides by heating the catalytic device under a second temperature condition when the high temperature control command is generated from the second processing unit. a catalytic device including a diesel oxidation catalyst and a selective catalytic reduction; an input unit configured to receive one or more elements of operation information of a vehicle among an engine operation time, an engine fuel consumption quantity, a vehicle trip distance, and sulfur oxides produced quantity; a memory unit configured to store a first operation information value for processing sulfur oxides and a second operation information value for processing sulfur oxides, wherein the first operation information value and the second operation information value are generated by evaluating the operation information received from the input unit; a first processing unit configured to determine whether the first operation information value stored in the memory unit reaches a predetermined first reference value, and command a low temperature control when the first operation information value reaches the first reference value; a second processing unit configured to determine whether the second operation information value stored in the memory unit reaches a predetermined second reference value, and command a high temperature control when the second operation information value reaches the predetermined second reference value; characterised by a sulfur oxides removal operating unit configured to remove a first sulfur oxides by heating the catalytic device under a first temperature condition when the low temperature control command is generated from the first processing unit, and remove the first sulfur oxides and a second sulfur oxides which is different from the first sulfur oxides and removed at a higher temperature than the first sulfur oxides by heating the catalytic device under a second temperature condition when the high temperature control command is generated from the second processing unit.