The centrosome is normally thought to determine the cell center and to dictate the formation of a radial array of microtubules that defines the spatial organization of cytoplasm. However, experiments indicate the existence of a mechanism for organization of a centered microtubule array that is independent of the centrosome. Here, we formulate a model of treadmilling dynamics of non-centrosomal microtubules that predicts a spontaneously established, polarized distribution of microtubule orientation. Based on this model, we propose that the autonomous ability of non-centrosomal microtubules to form a polarized array arises from their treadmilling within the space constrained by the cell boundary.