Dynamic nuclei are involved in a wide variety of fundamental biological processes including cell migration, cell division and fertilization. Here, we develop a mathematical model, in combination with live-cell imaging at high temporal resolution, to quantitatively elucidate how the linear and rotational motions of the nucleus are governed by the stochastic dynamics of the microtubule cytoskeleton. Our simulation and experimental results demonstrate that microtubule rescue and catastrophe frequencies are the decisive factors in regulating the nuclear movement. Lower rescue and catastrophe frequencies can lead to significantly larger angular and translational oscillations of the nucleus. In addition, our model also suggests that the stochastic dynamics of individual spatially distributed microtubules works collectively as a restoring force to maintain nuclear centering and hence ensures symmetric cell division, in excellent agreement with direct experimental observations.