Provided are a braking control system for a vehicle which is controlled in a priority order, and a method of the same. A braking control system for a vehicle equipped with an electronic brake at each wheel includes a first control unit controlling the operation of a first electronic brake mounted at a front-left wheel and a second electronic brake mounted at a front-right wheel in response to braking signals, and a second control unit controlling the operation of a third electronic brake mounted at a rear-left wheel and a fourth electronic brake mounted at a rear-right wheel in response to the braking signals. In this configuration, when a fail occurs in any one of the first and second control units, the other control unit selectively controls at least one or more of the first to fourth electronic brakes, in accordance with predetermined logic.