A control device of an internal combustion engine, comprising: a variable geometry turbocharger formed of a turbine having variable vanes that vary exhaust passage area, which is disposed in an exhaust passage of an internal combustion engine installed in a vehicle, and a compressor that is disposed in an intake passage and driven by the turbine; an exhaust-gas recirculation passage that is interposed between the exhaust passage and the intake passage and guides exhaust gas to the intake passage; an exhaust-gas recirculation valve that controls a flow rate of exhaust gas flowing through the exhaust-gas recirculation passage; a vehicle-deceleration detecting unit that detects the deceleration of a vehicle; an injection-amount detecting unit that detects a fuel injection amount of the internal combustion engine; and a control unit that controls an opening degree of variable vanes of the variable geometry turbocharger and the opening degree of the exhaust-gas recirculation valve, and, when the vehicle deceleration is detected, the control unit sets the opening degree of the variable vanes of the variable geometry turbocharger into a fully open position and further sets the opening degree of the exhaust-gas recirculation valve according to the fuel injection amount; characterized in that the control unit decreases the opening degree of the exhaust-gas recirculation valve when the fuel injection amount is high, and increases the opening degree of the exhaust-gas recirculation valve along with decrease in the fuel injection amount, and further sets the opening degree of the exhaust-gas recirculation valve into the fully open position when the fuel injection amount reaches zero. a variable geometry turbocharger formed of a turbine having variable vanes that vary exhaust passage area, which is disposed in an exhaust passage of an internal combustion engine installed in a vehicle, and a compressor that is disposed in an intake passage and driven by the turbine; an exhaust-gas recirculation passage that is interposed between the exhaust passage and the intake passage and guides exhaust gas to the intake passage; an exhaust-gas recirculation valve that controls a flow rate of exhaust gas flowing through the exhaust-gas recirculation passage; a vehicle-deceleration detecting unit that detects the deceleration of a vehicle; an injection-amount detecting unit that detects a fuel injection amount of the internal combustion engine; and a control unit that controls an opening degree of variable vanes of the variable geometry turbocharger and the opening degree of the exhaust-gas recirculation valve, and, a vehicle-deceleration detecting unit that detects the deceleration of a vehicle; an injection-amount detecting unit that detects a fuel injection amount of the internal combustion engine; and a control unit that controls an opening degree of variable vanes of the variable geometry turbocharger and the opening degree of the exhaust-gas recirculation valve, and, when the vehicle deceleration is detected, the control unit sets the opening degree of the variable vanes of the variable geometry turbocharger into a fully open position and further sets the opening degree of the exhaust-gas recirculation valve according to the fuel injection amount; characterized in that the control unit decreases the opening degree of the exhaust-gas recirculation valve when the fuel injection amount is high, and increases the opening degree of the exhaust-gas recirculation valve along with decrease in the fuel injection amount, and further sets the opening degree of the exhaust-gas recirculation valve into the fully open position when the fuel injection amount reaches zero. <EOS>