Spindle assembly required during mitosis depends on microtubule polymerization. We demonstrate that the evolutionarily conserved low-complexity protein, BuGZ, undergoes phase transition or coacervation to promote assembly of both spindles and their associated components. BuGZ forms temperature-dependent liquid droplets alone or on microtubules in physiological buffers. Coacervation in vitro or in spindle and spindle matrix depends on hydrophobic residues in BuGZ. BuGZ coacervation and its binding to microtubules and tubulin are required to promote assembly of spindle and spindle matrix in Xenopus egg extract and in mammalian cells. Since several previously identified spindle-associated components also contain low-complexity regions, we propose that coacervating proteins may be a hallmark of proteins that comprise a spindle matrix that functions to promote assembly of spindles by concentrating its building blocks.