A control apparatus for an internal combustion engine that controls an internal combustion engine that has a turbocharger provided in an intake passage, an actuator which is configured to change an operating state of the turbocharger to adjust a turbocharging pressure, a throttle provided downstream relative to the turbocharger in the intake passage, and a catalyst having a NOx storage-reduction capacity which is provided in an exhaust passage, and that is an internal combustion engine which is capable of lean burn operation according to a predetermined air-fuel ratio that is leaner in fuel than a theoretical air-fuel ratio, wherein, during execution of the lean burn operation, the control apparatus executes a rich spike that supplies a reducing agent to the catalyst by decreasing an air amount by means of the throttle and also making a combustion air-fuel ratio richer in fuel than the theoretical air-fuel ratio, the control apparatus comprising: first control means for executing first quantity of state control that executes the rich spike while actuating the actuator so as to decrease a turbocharging pressure relative to a turbocharging pressure before execution of the rich spike, and after completion of the rich spike, actuates the actuator to raise the turbocharging pressure again, adjusts the combustion air-fuel ratio to the theoretical air-fuel ratio while suppressing an air amount by means of the throttle until the turbocharging pressure is restored to a pressure that is equal to the turbocharging pressure before execution of the rich spike, and upon the turbocharging pressure being restored to a pressure that is equal to the turbocharging pressure before execution of the rich spike, increases the air amount by means of the throttle and returns the combustion air-fuel ratio to the predetermined air-fuel ratio; second control means for executing second quantity of state control that executes the rich spike while actuating the actuator so as to maintain the turbocharging pressure at a pressure thereof prior to execution of the rich spike, and after completion of the rich spike, increases the air amount by means of the throttle and returns the combustion air-fuel ratio to the predetermined air-fuel ratio; and selection means for, in a case where a timing arrives for executing the rich spike in an operating region in which turbocharging by the turbocharger is performed, selecting, between execution of the first quantity of state control by the first control means and execution of the second quantity of state control by the second control means, the one which results in a smaller fuel consumption quantity. first control means for executing first quantity of state control that executes the rich spike while actuating the actuator so as to decrease a turbocharging pressure relative to a turbocharging pressure before execution of the rich spike, and after completion of the rich spike, actuates the actuator to raise the turbocharging pressure again, adjusts the combustion air-fuel ratio to the theoretical air-fuel ratio while suppressing an air amount by means of the throttle until the turbocharging pressure is restored to a pressure that is equal to the turbocharging pressure before execution of the rich spike, and upon the turbocharging pressure being restored to a pressure that is equal to the turbocharging pressure before execution of the rich spike, increases the air amount by means of the throttle and returns the combustion air-fuel ratio to the predetermined air-fuel ratio; second control means for executing second quantity of state control that executes the rich spike while actuating the actuator so as to maintain the turbocharging pressure at a pressure thereof prior to execution of the rich spike, and after completion of the rich spike, increases the air amount by means of the throttle and returns the combustion air-fuel ratio to the predetermined air-fuel ratio; and selection means for, in a case where a timing arrives for executing the rich spike in an operating region in which turbocharging by the turbocharger is performed, selecting, between execution of the first quantity of state control by the first control means and execution of the second quantity of state control by the second control means, the one which results in a smaller fuel consumption quantity.