Disclosed is a corner module apparatus for a vehicle. The corner module apparatus includes processors configured to receive a braking initiation manipulation input of a vehicle from a driver. The corner module apparatus also includes a controller configured to perform braking of the vehicle by independently controlling steering of four wheels of the vehicle based on a direction angle when the braking initiation manipulation input is received by the one or more processors in a state in which the vehicle is positioned on the slope. The direction angle is an angle between an inclined direction of a slope and a longitudinal direction of the vehicle.