An exhaust gas cleaning apparatus includes a combustion mode shifter that shifts combustion in a cylinder of an engine from a lean-burn mode to a rich-burn mode for enabling a LNT to reduce NOx contained in the exhaust gas. The combustion mode shifter is configured to: estimate a torque-producing fuel quantity for a fuel injection made by a fuel injector when the combustion is in the lean-burn mode; estimate an excess oxygen ratio for an upcoming fuel injection during the shifting of the combustion from the lean-burn mode to the rich-burn mode; estimate a fuel burning percentage for the upcoming fuel injection based on the excess oxygen ratio; set a command injection quantity for the upcoming fuel injection based on the torque-producing fuel quantity and the fuel burning percentage; and control the fuel injector to inject the command injection quantity of fuel into the cylinder in the upcoming fuel injection.