PURPOSE: To eliminate any delay of a control supercharging pressure in following to a target supercharging pressure right after transfer from a single turbocharger to a plurality of turbochargers and to prevent the overshoot of a control supercharging pressure during acceleration in a plurality of turbocharger areas.

CONSTITUTION: The initial value of a duty ratio responding to a target supercharging pressure determined by a target supercharging pressure calculating means 60 is determined by an initial duty ratio calculating means 61. Control is executed such that by correcting the initial value of a duty ratio, determined by the initial duty ratio calculating means 61, by means of a first duty ratio correcting means 62, a control supercharging pressure is caused to follow a target supercharging pressure. Further, an initial valve of a during ratio right after transfer from supercharging only by a main turbocharger to supercharging by two turbochargers is corrected to a value higher than that at a time, when acceleration during supercharging by both main and auxiliary turbochargers is started, by means of a second duty ratio correcting means 64.