A multistage supercharging system control apparatus for controlling a multistage supercharging system which comprises: a high-pressure turbo charger including a high-pressure turbine which is rotated and driven by exhaust gas, and a high-pressure compressor which pressurizes intake air which is rotated and driven by the high-pressure turbine so as to pressurize supply gas; a low-pressure turbo charger including a low-pressure turbine which is rotated and driven by exhaust gas at a location downstream of the high-pressure turbine with respect to an exhaust gas flow direction, and a low-pressure compressor which is rotated and driven by the low-pressure turbine so as to pressurize supply gas at a location upstream of the high-pressure compressor with respect to a supply gas flow direction; and an intake-exhaust passage (2, 3) configured such that a supercharging mode can be switched between a twin supercharging mode in which exhaust gas is supplied to the low-pressure turbine via the high-pressure turbine, whereby supercharging is performed by the low-pressure compressor and the high-pressure compressor, and a single supercharging mode in which exhaust gas is supplied to the low-pressure turbine while being caused to bypass the high-pressure turbine, whereby supercharging is performed by the low-pressure compressor, wherein the multistage supercharging system control apparatus comprises: single-mode supercharging pressure acquisition means for acquiring a single-mode supercharging pressure acquired value corresponding to a supercharging pressure generated by the entire multistage supercharging system operated in the single supercharging mode; and supercharging mode changeover means for prohibiting changeover from the single supercharging mode to the twin supercharging mode when the single-mode supercharging pressure acquired value is less than a target value of the pressure of supply gas at the outlet of the low-pressure compressor in the twin supercharging mode, and permitting the changeover from the single supercharging mode to the twin supercharging mode when the single-mode supercharging pressure acquired value is equal to or greater than the target value, characterized in that the single-mode supercharging pressure acquisition means acquires a low-pressure-side supercharging pressure acquired value corresponding to the pressure of supply gas at the outlet of the low-pressure compressor. a high-pressure turbo charger including a high-pressure turbine which is rotated and driven by exhaust gas, and a high-pressure compressor which pressurizes intake air which is rotated and driven by the high-pressure turbine so as to pressurize supply gas; a low-pressure turbo charger including a low-pressure turbine which is rotated and driven by exhaust gas at a location downstream of the high-pressure turbine with respect to an exhaust gas flow direction, and a low-pressure compressor which is rotated and driven by the low-pressure turbine so as to pressurize supply gas at a location upstream of the high-pressure compressor with respect to a supply gas flow direction; and an intake-exhaust passage (2, 3) configured such that a supercharging mode can be switched between a twin supercharging mode in which exhaust gas is supplied to the low-pressure turbine via the high-pressure turbine, whereby supercharging is performed by the low-pressure compressor and the high-pressure compressor, and a single supercharging mode in which exhaust gas is supplied to the low-pressure turbine while being caused to bypass the high-pressure turbine, whereby supercharging is performed by the low-pressure compressor, single-mode supercharging pressure acquisition means for acquiring a single-mode supercharging pressure acquired value corresponding to a supercharging pressure generated by the entire multistage supercharging system operated in the single supercharging mode; and supercharging mode changeover means for prohibiting changeover from the single supercharging mode to the twin supercharging mode when the single-mode supercharging pressure acquired value is less than a target value of the pressure of supply gas at the outlet of the low-pressure compressor in the twin supercharging mode, and permitting the changeover from the single supercharging mode to the twin supercharging mode when the single-mode supercharging pressure acquired value is equal to or greater than the target value,