The invention relates to a variable air volume control apparatus which compensates an open area ratio to be in direct proportion to an opening ratio at a low opening ratio range according to an open angle of a damper blade to achieve accurate and precise air volume control. The variable air volume control apparatus includes a damper blade disposed rotatably within the duct for opening or closing an air flow path and an actuator for rotating the damper blade. The apparatus also includes an air flow path expansion mechanism having a curved surface for expanding the air flow path in accordance with an open angle of the damper blade. The invention allows obtaining the open area ratio in direct proportion to the opening ratio at the low opening ratio range through simple structural improvements, thereby improving linear characteristics of an air volume change ratio with respect to the opening ratio to more accurately and precisely control the air volume.