A six-stroke engine includes a cylinder, a piston, a cylinder head, a combustion chamber, an intake port, an exhaust port, an intake valve, an exhaust valve, a fuel injector, and an ignition plug. The six-stroke engine includes a valve gear that operates the intake valve and the exhaust valve to execute an intake stroke, a compression stroke with ignition, an expansion stroke with combustion, an exhaust stroke, an expansion stroke without combustion, and a compression stroke without ignition. The valve gear opens, only for a predetermined period of time while the piston is located at top dead center, at least one of the intake valve and the exhaust valve within a period from the exhaust stroke to the intake stroke. A valve overlap state is produced at least once within the period from the exhaust stroke to the intake stroke.