Abstract: The invention provides a control method of intending to improve a heat efficiency by an Atkinson cycle, improve a charging efficiency, improve an efficiency of a supercharger and increase a freedom of cam design. In particular, the invention relates to a control method of opening and closing a valve in an internal combustion engine with supercharger. An effective compression ratio is decreased by temporarily re-opening an exhaust valve in a compression stroke first stage, whereby a heat efficiency is improved without excessively increasing a cylinder internal pressure. Preferably, an exhaust valve re-opening time is set such that the effective compression ratio/expansion ratio is within a range from 0.5 to 0.9. Further, an exhaust valve is not temporarily opened in a compression stroke first stage, at a time of starting or driving under a low load, and the Atkinson cycle in accordance with the re-opening of the exhaust valve is achieved at a time of driving under a high load.