The boost pressure of a blower such as a turbocharger or a supercharger which is driven by the exhaust gas or the power output from an engine is controlled under closed-loop control when the boost pressure is in a steady state, and under open-loop control when the boost pressure is in a transient state. When the boost pressure is in the transient state, the open-loop control which may be map control is carried out for relatively good accuracy and high stability. When the boost pressure is in the steady state, the closed-loop control, i.e., highly accurate feedback control, is effected. Therefore, an improved response and stability can be achieved in boost pressure control.