The dynamic organization of microtubules into parallel arrays allows interphase cells to set up multi-lane highways for intracellular transport and M-phase cells to build the mitotic and meiotic spindles. Here we show that a minimally reconstituted system composed of Klp2, a kinesin-14 from the fission yeast Schizosaccharomyces pombe, together with microtubules assembled from purified S. pombe tubulin, autonomously assembles bundles of parallel microtubules. Bundles form by an ATP-dependent sorting mechanism that requires the full-length Klp2 motor. By this mechanism, antiparallel-overlapped microtubules slide over one another until they dissociate from the bundles, whereas parallel-overlapped microtubules are selectively trapped by an energy-dissipating force-balance mechanism. Klp2-driven microtubule sorting provides a robust pathway for the organization of microtubules into parallel arrays. In vivo evidence indicates that Klp2 is required for the proper organization of S. pombe interphase microtubules into bipolar arrays of parallel-overlapped microtubules, suggesting that kinesin-14-dependent microtubule sorting may have wide biological importance.