A tire-pressure control apparatus includes an air pump driven by a rotating wheel to supply compressed air to a tire air chamber, a mechanical control valve that permits and prohibits supply of compressed air from the air pump to the tire air chamber, a valve-state detection sensor that detects the state of the control valve, a wheel speed sensor that detects rotational speed of the wheel, and an electric control unit (ECU). The ECU calculates a quantity of compressed air supplied from the air pump to the tire air chamber during a permission-state retention time, during which the control valve is in the permission state, and calculates an average leaked air quantity per unit time in a single cycle starting when the control valve enters a prohibition state and ending when the control valve again enters the prohibition state after entering the permission state.