An engine system is provided, which includes a cylinder block, a cylinder head, a piston, a main combustion chamber, a subchamber, an injector that injects fuel into the main combustion chamber, a main spark plug that ignites a mixture gas inside the main combustion chamber, a subspark plug that ignites the mixture gas inside the subchamber, and a controller electrically connected to the injector, the main spark plug and the subspark plug. When an engine load is above a given reference load, the controller controls, in a low-speed range below a given reference engine speed, the ignition devices so that the subignition is performed after the main ignition, and the controller controls, in a high-speed range exceeding the reference engine speed, the ignition devices so that only the subignition is performed, or so that the main ignition is performed at the same timing as or after the subignition.