To solve or relax the jerky movement of a vehicle generated during traveling at low speed.

In fuel cut control over an internal combustion engine, when an accelerator opening θ is set to a threshold or below, it is determined as one of fuel cut start conditions. When a variation or a rate of change Δθ/Δt per unit time in the accelerator opening θ is below a predetermined value A, the threshold is set to a value θ1 smaller than a threshold θ2 when it is not below the predetermined value. Thereby, it becomes possible to reduce fuel cut start frequency when slightly depressing an accelerator pedal during the traveling at low speed and to avoid occurrence of the jerky movement due to frequency of fuel cut.