Provided is a brake control apparatus mounted in a vehicle with a plurality of wheels, the brake control apparatus including: a actuator configured to apply a braking torque to the plurality of wheels; and a controller configured to control the actuator to apply a first braking torque to a first wheel of the plurality of wheels, based on a spin of the first wheel being greater than or equal to a target spin, and to control the actuator to apply a second braking torque to the plurality of wheels based on a displacement of a brake pedal of the vehicle while applying the first braking torque to the first wheel, wherein the controller stepwise or linearly increases a braking torque applied to a second wheel of the plurality of wheels up to the second braking torque.