In-cylinder injection type spark-ignition internal combustion engine and control method thereof

An in-cylinder injection type spark-ignition internal combustion engine and a control method thereof realize a stabilized stratified-charge combustion by setting a large lift amount to an intake valve 23 when the engine 1 is cold-started and by executing a compression stroke injection. At this time, warming-up capability of a catalyst is improved by delaying an ignition timing.