A stereoscopic display device, a method and apparatus for controlling the stereoscopic display device and a storage medium are provided. The stereoscopic display device includes a display panel and a varifocal lens array. The varifocal lens array is on a side of display panel where an image surface is; the varifocal lens array comprises at least two varifocal lenses arranged in an array, wherein any one of the varifocal lenses corresponds to at least one sub-pixel region on the display panel, and the at least two varifocal lenses are configured such that colored lights of the corresponding sub-pixel regions form images having different image distances on a side of the varifocal lenses near the display panel; wherein the image surface of the display panel is a surface of the display panel where colored light is formed. The effects of higher resolution and brightness of the stereoscopic display device are achieved.