A control apparatus for a vehicle, the vehicle including an internal combustion engine, a drive wheel, a non-drive wheel, a stepped automatic transmission, a coupling device, and a braking device, the stepped automatic transmission being configured to transmit power generated by the internal combustion engine to the drive wheel, the coupling device being interposed between the internal combustion engine and the stepped automatic transmission, the coupling device being configured to transmit the power generated by the internal combustion engine to the stepped automatic transmission such that the vehicle makes a creep travel, the braking device being configured to apply a braking force to the drive wheel and the non-drive wheel, the control apparatus comprising an electronic control unit configured to: control the internal combustion engine and the stepped automatic transmission; execute a target idle speed control for controlling the internal combustion engine such that an engine speed matches a target idle speed when an operation state of the internal combustion engine is an idle operation state; set an upper limit value of the target idle speed when a specified low μ road control condition is established while the braking device acts on the vehicle, such that the upper limit value when the stepped automatic transmission is in first gear is smaller than the upper limit value when the stepped automatic transmission is in a second gear; and set a change amount per unit time of the upper limit value such that the change amount per unit time when the stepped automatic transmission shifts from first gear to second gear is smaller than the change amount per unit time when the stepped automatic transmission shifts from second gear to first gear. an electronic control unit configured to: control the internal combustion engine and the stepped automatic transmission; execute a target idle speed control for controlling the internal combustion engine such that an engine speed matches a target idle speed when an operation state of the internal combustion engine is an idle operation state; set an upper limit value of the target idle speed when a specified low μ road control condition is established while the braking device acts on the vehicle, such that the upper limit value when the stepped automatic transmission is in first gear is smaller than the upper limit value when the stepped automatic transmission is in a second gear; and set a change amount per unit time of the upper limit value such that the change amount per unit time when the stepped automatic transmission shifts from first gear to second gear is smaller than the change amount per unit time when the stepped automatic transmission shifts from second gear to first gear. control the internal combustion engine and the stepped automatic transmission; execute a target idle speed control for controlling the internal combustion engine such that an engine speed matches a target idle speed when an operation state of the internal combustion engine is an idle operation state; set an upper limit value of the target idle speed when a specified low μ road control condition is established while the braking device acts on the vehicle, such that the upper limit value when the stepped automatic transmission is in first gear is smaller than the upper limit value when the stepped automatic transmission is in a second gear; and set a change amount per unit time of the upper limit value such that the change amount per unit time when the stepped automatic transmission shifts from first gear to second gear is smaller than the change amount per unit time when the stepped automatic transmission shifts from second gear to first gear.