A control apparatus for an internal combustion engine with a supercharger including a turbine (321, 322) driven by exhaust gas flowing through an exhaust path of the internal combustion engine and supercharging the internal combustion engine with air flowing through an intake path using a compressor (311, 312) coupled to the turbine (321, 322), the control apparatus comprising: a supercharging pressure control unit adjusting a supercharging pressure for supercharging the internal combustion engine with air to a target supercharging pressure by changing an opening degree of an exhaust flow rate regulating valve (321a, 321b, 322a) adjusting a flow rate of the exhaust gas flowing through the exhaust path based on a physical model including a valve restriction expression and a conversion efficiency expression for the turbine and the compressor of the internal combustion engine with a supercharger, the supercharging pressure control unit, in response to a change in the accelerator pedal position in which acceleration is instructed, forcibly fully closing the exhaust flow rate regulating valve continuously when it determines, based on the physical model, that the supercharging pressure cannot immediately reach the target supercharging pressure unless the exhaust flow rate regulating valve is fully closed when in case of a middle load area the rotational frequency of the turbine estimated based on the model is lower than a target value and the difference between the rotational frequency and the target value is more than a threshold; a supercharging pressure state determination unit determining whether an actual supercharging pressure is equal to or more than the target supercharging pressure when the opening degree of the exhaust flow rate regulating valve (321a, 321b, 322a) is put in a fully closing state; and a valve opening release unit changing the opening degree of the exhaust flow rate regulating valve (321a, 321b, 322a) in an opening direction from the fully closing state when the actual supercharging pressure is equal to or more than the target supercharging pressure when the opening degree of the exhaust flow rate regulating valve (321a, 321b, 322a) is put in the fully closing state. a supercharging pressure control unit adjusting a supercharging pressure for supercharging the internal combustion engine with air to a target supercharging pressure by changing an opening degree of an exhaust flow rate regulating valve (321a, 321b, 322a) adjusting a flow rate of the exhaust gas flowing through the exhaust path based on a physical model including a valve restriction expression and a conversion efficiency expression for the turbine and the compressor of the internal combustion engine with a supercharger, the supercharging pressure control unit, in response to a change in the accelerator pedal position in which acceleration is instructed, forcibly fully closing the exhaust flow rate regulating valve continuously when it determines, based on the physical model, that the supercharging pressure cannot immediately reach the target supercharging pressure unless the exhaust flow rate regulating valve is fully closed when in case of a middle load area the rotational frequency of the turbine estimated based on the model is lower than a target value and the difference between the rotational frequency and the target value is more than a threshold; a supercharging pressure state determination unit determining whether an actual supercharging pressure is equal to or more than the target supercharging pressure when the opening degree of the exhaust flow rate regulating valve (321a, 321b, 322a) is put in a fully closing state; and a valve opening release unit changing the opening degree of the exhaust flow rate regulating valve (321a, 321b, 322a) in an opening direction from the fully closing state when the actual supercharging pressure is equal to or more than the target supercharging pressure when the opening degree of the exhaust flow rate regulating valve (321a, 321b, 322a) is put in the fully closing state.