An exhaust system for an internal-combustion engine comprises an exhaust bypass in parallel with an upstream portion of a main exhaust path having a main catalytic converter in a downstream portion thereof; an exhaust bypass catalytic converter provided in the exhaust bypass; and a flow path switching valve for blocking the main exhaust path at the upstream portion thereof. The exhaust system includes an ignition timing adjustment mechanism for adjusting ignition timing to delay sparking when the flow path switching valve is switched from the closed condition to the open condition thereof. A control method for the exhaust system is also disclosed.