In order to improve size uniformity of InAs quantum dots (QDs) on (001) InP substrates using droplet heteroepitaxy by metal-organic vapor phase epitaxy, the authors carried out the growth of InAs QDs on size-controlled linear mesa-structure templates fabricated by using selective-area growth technique and surrounded by facet planes. InAs QDs preferentially formed on the (001) top surface facet. The maximum size of QD was limited by the width of the top surface. On the other hand, the minimum size was defined by the practically critical size. These facts imply that the narrow width of the top surface of templates controls the dispersion of size distribution. The authors obtained the narrow photoluminescence peak from the size-controlled InAs QDs with full width at half maximum of 85meV at around 1.5μm wavelength.