A supercharging system for an internal combustion engine, comprising: an internal combustion engine; a plurality of turbochargers (10A, 10B) driven by exhaust gas from the internal combustion engine; an intake flow-passage switching valve configured to be capable of switching an intake flow passage of the internal combustion engine; an exhaust flow-passage switching valve configured to be capable of switching an exhaust flow passage of the internal combustion engine; a target boost-pressure calculation part configured to calculate a target boost pressure on the basis of an operational state of the internal combustion engine; a boost-pressure detection part configured to detect a boost pressure of the plurality of turbochargers (10A, 10B); and a control part configured to control the intake flow-passage switching valve and the exhaust flow-passage switching valve on the basis of a first control index θ which is calculated on the basis of the target boost pressure and the boost pressure, characterized in that the first control index θ 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 and set so as to depend only on the opening degree of the compressor bypass valve in the range of 0≤θ<1, and only on the opening degree of the exhaust flow-rate control valve in the range of 1≤θ<2, wherein the supercharging system further comprises a conversion table for converting the first control index θ into a second control index having a linear property with respect to the boost pressure, and wherein the control part is configured to convert the second control index calculated on the basis of the target boost pressure and the boost pressure into the first control index θ with the conversion table, and to control the intake flow-passage switching valve and the exhaust flow-passage switching valve on the basis of the first control index θ. an internal combustion engine; a plurality of turbochargers (10A, 10B) driven by exhaust gas from the internal combustion engine; an intake flow-passage switching valve configured to be capable of switching an intake flow passage of the internal combustion engine; an exhaust flow-passage switching valve configured to be capable of switching an exhaust flow passage of the internal combustion engine; a target boost-pressure calculation part configured to calculate a target boost pressure on the basis of an operational state of the internal combustion engine; a boost-pressure detection part configured to detect a boost pressure of the plurality of turbochargers (10A, 10B); and a control part configured to control the intake flow-passage switching valve and the exhaust flow-passage switching valve on the basis of a first control index θ which is calculated on the basis of the target boost pressure and the boost pressure, characterized in that the first control index θ 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 and set so as to depend only on the opening degree of the compressor bypass valve in the range of 0≤θ<1, and only on the opening degree of the exhaust flow-rate control valve in the range of 1≤θ<2, wherein the supercharging system further comprises a conversion table for converting the first control index θ into a second control index having a linear property with respect to the boost pressure, and wherein the control part is configured to convert the second control index calculated on the basis of the target boost pressure and the boost pressure into the first control index θ with the conversion table, and to control the intake flow-passage switching valve and the exhaust flow-passage switching valve on the basis of the first control index θ.