An apparatus for controlling exhaust of an engine having at least one cylinder and a piston disposed in the cylinder and connected to a crankshaft, the apparatus comprising: catalyst means for removing pollutants from exhaust emitted by the engine; fuel injection means for injecting fuel at a fuel pressure into the cylinder; intake valve means for supplying an intake air quantity of air to the cylinder; ignition means for igniting a mixture of the fuel and the air in the cylinder at an ignition timing; intake valve adjustment means for adjusting the intake air quantity by changing a characteristic of the intake valve means; and control means for controlling the fuel injection means, the ignition means, and the intake valve adjustment means, the control means being arranged to detect whether or not a request is present for activating the catalyst means when the engine is started, the control means being further arranged to determine whether or not the fuel pressure is greater than or equal to a predetermined pressure; wherein when the control means detects that a request is not present for activating the catalyst means when the engine is started, the engine is operated in a homogeneous combustion mode in which the fuel is injected during the intake stroke and in which ignition timing is set to ignite the fuel-air mixture before compression top dead center; wherein when the control means detects that a request is present for activating the catalyst means when the engine is started and that the fuel pressure is greater than or equal to the predetermined fuel pressure, the engine is operated in a retarded combustion mode in which the ignition timing is retarded to ignite the fuel-air mixture after compression top dead center and after the fuel has been injected, the intake valve adjustment means being controlled so that the intake air quantity is larger than the intake air quantity when the request for activating the catalyst means is not present; and wherein when the control means detects that a request is present for activating the catalyst means when the engine is started and that the fuel pressure is not greater than or equal to the predetermined fuel pressure, the engine is operated in the homogeneous combustion mode, the intake valve adjustment means being controlled so that the intake air quantity is larger than the intake air quantity in the homogeneous combustion mode when the request for activating the catalyst means is not present. catalyst means for removing pollutants from exhaust emitted by the engine; fuel injection means for injecting fuel at a fuel pressure into the cylinder; intake valve means for supplying an intake air quantity of air to the cylinder; ignition means for igniting a mixture of the fuel and the air in the cylinder at an ignition timing; intake valve adjustment means for adjusting the intake air quantity by changing a characteristic of the intake valve means; and control means for controlling the fuel injection means, the ignition means, and the intake valve adjustment means, the control means being arranged to detect whether or not a request is present for activating the catalyst means when the engine is started, the control means being further arranged to determine whether or not the fuel pressure is greater than or equal to a predetermined pressure;