The dimensions and morphologies of quantum nanostructures are keys to controlling an operating wavelength to a desirable wavelength range due to the quantum effect. The dimension and morphology evolutions of InSb/InAs quantum nanostructures grown by molecular beam epitaxy with respect to the number of InSb monolayers (MLs) are investigated. The formation of the quantum nanostructures is dominated by lateral growth, in which the morphology is further elongated as the number of MLs is increased. Such an anisotropic growth is explained by the difference in the surface energy along each direction, which corresponds to different atomic arrangements in the crystalline structure of InSb. Cross‐sectional transmission electron microscopic images show a reduction in the lateral dimension and an increase in the height of the embedded InSb quantum nanostructures when they are embedded in the InAs matrix. The results herein provide a means for obtaining the precise control over dimensions and morphologies of the InSb/InAs nanostructures, which is essential for extending the operating wavelength further into the mid‐infrared region.