The turning control apparatus for a vehicle has a driving torque controlling mechanism adjusting driving torque of left and right wheels. The apparatus includes a maximum-yaw momentum value calculating means having means for estimating an outside-wheel gripping capacity, which is capacity of adhesive friction between the outside-wheel and a road surface, and an inside-wheel gripping capacity, which is capacity of adhesive friction between the inside-wheel and the road surface, and means for calculating a torque adjustment limiting value indicating an adjustment amount of driving torque by the driving torque controlling mechanism so that the adjustment amount does not exceed the gripping capacity. The maximum-yaw momentum value calculating means sets the maximum-yaw momentum value indicating possible yaw momentum, which is estimated if the driving torque is adjusted along with the torque-adjustment-limit value calculated by the torque adjustment limiting value calculating means.