An engine system may include main exhaust ports fluidly communicated with each combustion chamber, main exhaust valves opening and closing each main exhaust port, a main exhaust manifold connected with the main exhaust ports, scavenge exhaust ports fluidly communicated with the each combustion chamber, scavenge valves opening and closing the each scavenge exhaust port, a scavenge manifold connected with the scavenge exhaust ports, in which at least a part of an exhaust gas passing through the scavenge manifold is re-circulated to the combustion chamber to be burned.