Provided is a control device for an internal combustion engine that can execute a sulfur purge in a favorable manner under all conditions without complicating the control action or the engine structure. The process comprises detecting a temperature of the NOx catalytic converter, detecting an exhaust air fuel ratio in the catalytic converter, computing a target exhaust air fuel ratio according to a detected temperature of the NOx catalytic converter, and controlling a fuel injection valve so as to make an actual exhaust fuel ratio agree with the target exhaust air fuel ratio. If the temperature of the NOx catalytic converter is not high enough to enable a sulfur purge, a temperature increase control is executed to increase the temperature of the NOx catalytic converter by suitably changing various engine parameters.