Dynamic properties of microtubules contribute to the establishment of spatial order within cells. In the fission yeast Schizosaccharomyces pombe, interphase cytoplasmic microtubules are organized into antiparallel bundles that attach to the nuclear envelope and are needed to position the nucleus at the geometric center of the cell. Here, we show that after the nucleus is displaced by cell centrifugation, these microtubule bundles efficiently push the nucleus back to the center. Asymmetry in microtubule number, length, and dynamics contributes to the generation of force responsible for this unidirectional movement. Notably, microtubules facing the distal cell tip are destabilized when the microtubules in the same bundle are pushing from the proximal cell tip. The CLIP-170-like protein tip1p and the microtubule-bundling protein ase1p are required for this asymmetric regulation of microtubule dynamics, indicating contributions of factors both at microtubule plus ends and within the microtubule bundle. Mutants in these factors are defective in nuclear movement. Thus, cells possess an efficient microtubule-based engine that produces and senses forces for centering the nucleus. These studies may provide insights into mechanisms of asymmetric microtubule behaviors and force sensing in other processes such as chromosome segregation and cell polarization.