Desulfurization method

A desulfurization method comprising:

• operating an engine to warm up an NOx storage-reduction catalyst provided in an exhaust passage coupled to the engine;
• controlling the engine so that an excess air ratio of the engine becomes a target value that is lower than 1 when a temperature of the NOx storage-reduction catalyst reaches a temperature at which the NOx storage-reduction catalyst is capable of reducing sulfur components stored in the NOx storage-reduction catalyst;
• stopping the engine after the excess air ratio of the engine is controlled to the target value;
• closing the exhaust passage at a downstream side of the NOx storage-reduction catalyst after stopping the engine;
• and
• maintaining the exhaust passage closed for a predetermined period such that the sulfur components stored in the NOx storage-reduction catalyst are removed while the engine is stopped.