A braking control system and method of a vehicle are configured to safely stop the vehicle by determining whether a brake line fails via detecting a change in braking pressure and compensating for braking force through an engaging operation of an electric parking brake (EPB) when determining that the brake line fails in association with driver manipulation of the brake pedal. The braking control system includes: a vehicle speed detector; a wheel lock detector; a brake pedal operation detector that determines whether a brake pedal is operated; a brake line failure detector that determines whether the brake line fails when the brake pedal is operated; and a controller configured to engage the EPB when a current vehicle speed is equal to or greater than a predetermined vehicle speed, a current state is a wheel-unlock state, and the brake line fails.