A supercharging system for an internal combustion engine controls an intake flow-passage switching valve and an exhaust flow-passage switching valve disposed in an intake flow passage and an exhaust flow passage, respectively, on the basis of a first control index which is calculated on the basis of a target boost pressure calculated on the basis of an operational state of the internal combustion engine and an actual boost pressure. The first control index is calculated from an arithmetic expression including opening degrees of the intake flow-passage switching valve and the exhaust flow-passage switching valve as variables.