Polyploid cells endoreplicate their DNA through a modified cell cycle that skips mitosis as part of their differentiation programs. Upon cell-cycle exit and differentiation, non-centrosomal sites govern microtubule distribution in most cells. Little is known on how polyploid cells, differentiated but cycling, organize their microtubules. We show that microtubules in Drosophila adipocytes and other polyploid tissues form a dense perinuclear cortex responsible for nuclear size and position. Confirming a relation between this perinuclear cortex and the polyploid endocycle, polyploidization of normally diploid cells was sufficient for cortex formation. A critical component of the perinuclear microtubule organizer (pnMTOC) is Shot, absence of which caused collapse of the perinuclear network into a condensed organizer through kinesin-dependent microtubule sliding. Furthermore, this ectopic organizer was capable of directing partial assembly of a deeply disruptive cytokinesis furrow. In all, our study revealed the importance of perinuclear microtubule organization for stability of endocycling Drosophila cells.