A control device of a vehicle capable of improving acceleration responsiveness and suppressing increase in the NOx emission amount when a required torque is increased during a steady lean operation. A target air-fuel ratio (AFCMD) is set according to an accelerator pedal operation of a driver. When the driver depresses an accelerator pedal to make an acceleration request during the lean operation, in which the AFCMD is set to a predetermined lean air-fuel ratio (AFLN), air-fuel ratio reduction control is executed to reduce the AFCMD according to the acceleration request. In the air-fuel ratio reduction control, when the AFCMD calculated according to a required torque (TRQCMD) is smaller than a limit air-fuel ratio (AFLMT), the AFCMD is set to the AFLMT, and the AFLMT is set to a value smaller than the AFLN set in a steady state of the lean operation and larger than a theoretical air-fuel ratio (AFST).