A control apparatus of an internal combustion engine which includes: an EGR passage that connects between an intake passage and an exhaust passage of the internal combustion engine so as to circulate a part of an exhaust gas from the internal combustion engine as an EGR gas; an EGR valve that is arranged at a location between opposite ends of said EGR passage so as to adjust a flow rate of the EGR gas by adjusting a passage area of said EGR passage; a cutoff valve of a normally open type that opens and closes said EGR passage which is at an upstream side of said EGR valve and which is in the vicinity of a location at which said EGR passage is connected to said exhaust passage; an ECU; an opening and closing mechanism for opening and closing an intake valve and an exhaust valve, respectively, according to a command from the ECU;and a turbocharger that is arranged on the exhaust passage at a downstream side of a location at which said EGR passage is connected to said exhaust passage; wherein said ECU includes a change unit for opening and closing said cutoff valve; said change unit closes said cutoff valve at the time of a low rotation and high load operation of said internal combustion engine; said change unit opens said cutoff valve in other operating states; and said ECU sets opening and closing times of the intake valve and the exhaust valve such that a difference between a pressure in an intake port and a pressure in an exhaust port is the largest in a valve overlap period of the intake valve and the exhaust valve, characterized in that said ECU includes: a rotation number determination unit that determines whether the number of revolutions per unit time of said turbocharger exceeds a threshold value at the time when said cutoff valve is closed; and a prohibition unit that prohibits said cutoff valve from being closed, when a determination is made by said rotation number determination unit that the number of revolutions per unit time of said turbocharger exceeds the threshold value. an EGR passage that connects between an intake passage and an exhaust passage of the internal combustion engine so as to circulate a part of an exhaust gas from the internal combustion engine as an EGR gas; an EGR valve that is arranged at a location between opposite ends of said EGR passage so as to adjust a flow rate of the EGR gas by adjusting a passage area of said EGR passage; a cutoff valve of a normally open type that opens and closes said EGR passage which is at an upstream side of said EGR valve and which is in the vicinity of a location at which said EGR passage is connected to said exhaust passage; an ECU; an opening and closing mechanism for opening and closing an intake valve and an exhaust valve, respectively, according to a command from the ECU;and a turbocharger that is arranged on the exhaust passage at a downstream side of a location at which said EGR passage is connected to said exhaust passage; wherein said ECU includes a change unit for opening and closing said cutoff valve; said change unit closes said cutoff valve at the time of a low rotation and high load operation of said internal combustion engine; said change unit opens said cutoff valve in other operating states; and said ECU sets opening and closing times of the intake valve and the exhaust valve such that a difference between a pressure in an intake port and a pressure in an exhaust port is the largest in a valve overlap period of the intake valve and the exhaust valve, characterized in that said ECU includes: a rotation number determination unit that determines whether the number of revolutions per unit time of said turbocharger exceeds a threshold value at the time when said cutoff valve is closed; and a prohibition unit that prohibits said cutoff valve from being closed, when a determination is made by said rotation number determination unit that the number of revolutions per unit time of said turbocharger exceeds the threshold value. a rotation number determination unit that determines whether the number of revolutions per unit time of said turbocharger exceeds a threshold value at the time when said cutoff valve is closed; and a prohibition unit that prohibits said cutoff valve from being closed, when a determination is made by said rotation number determination unit that the number of revolutions per unit time of said turbocharger exceeds the threshold value.