A method for controlling an
internal combustion engine equipped with a
supercharger, including: in a case where when a compressor that rotates in conjunction with a
turbine that rotates by receiving energy from
exhaust gas discharged from the
internal combustion engine takes in
fresh air and supplies the
fresh air to an intake side of the
internal combustion engine, the
exhaust gas is purified by a catalyst disposed between an exhaust side of the internal
combustion engine and the
turbine, adjusting an opening degree of a waste
gate valve that is disposed in a
branch passage branched from an exhaust passage between the catalyst and the
turbine and merging with an
exhaust gas exhaust side of the turbine and adjusts a flow rate of the exhaust gas in the
branch passage to adjust a flow rate of the exhaust gas to be supplied to the turbine, or adjusting an opening degree of a variable
nozzle that adjusts a flow velocity of the exhaust gas to be supplied to the turbine, to increase a
back pressure of the exhaust gas to raise a temperature of the exhaust gas, thereby
warming up the catalyst; and setting the opening degree of the waste
gate valve to a maximum or substantially a maximum when the catalyst starts to be warmed up, and then decreasing the opening degree of the waste
gate valve as a temperature of the internal
combustion engine rises, or setting the opening degree of the variable
nozzle to a maximum or substantially a maximum when the catalyst starts to be warmed up, and then decreasing the opening degree of the variable
nozzle as the temperature of the internal
combustion engine rises.