A multi-stage turbo supercharging system includes: a bypass passage which bypasses a turbocharger from among a plurality of turbochargers, in an intake passage or an exhaust passage of the engine; a bypass valve disposed in the bypass passage; an operation mode selection part; a bypass valve opening degree map selection part configured to select at least one bypass valve opening degree map in accordance with the operation mode selected by the operation mode selection part, from among a plurality of bypass valve opening degree maps which represent respective relationships between a plurality of control parameters of the engine and an opening degree of the bypass valve; a bypass valve opening degree determination part configured to determine an opening degree command value for the bypass valve on the basis of the bypass valve opening degree map and control parameter information representing the plurality of control parameters; and a bypass valve opening degree control part configured to control the opening degree of the bypass valve on the basis of the opening degree command value for the bypass valve.