A stereoscopic image display apparatus capable of generating a cursor that moves according to user operation to allow stereoscopic view with a stereoscopic image including a set of images with parallax and capable of combining and displaying the cursor on the stereoscopic image acquires a parallax amount of the stereoscopic image at a location where the cursor is combined and displayed on the stereoscopic image and calculates a moving speed of the cursor. The stereoscopic image display apparatus determines whether the cursor is moving based on the calculated moving speed and generates the cursor including a certain predetermined value as the parallax amount of the cursor if it is determined that the cursor is moving. The stereoscopic image display apparatus generates the cursor by setting the parallax amount of the cursor to the parallax amount of the acquired stereoscopic image if it is determined that the cursor is not moving.