The ability of kinetochores (KTs) to maintain stable attachments to dynamic microtubule structures ('straight' during microtubule polymerization and 'curved' during microtubule depolymerization) is an essential requirement for accurate chromosome segregation. Here we show that the kinetochore-associated Ska complex interacts with tubulin monomers via the carboxy-terminal winged-helix domain of Ska1, providing the structural basis for the ability to bind both straight and curved microtubule structures. This contrasts with the Ndc80 complex, which binds straight microtubules by recognizing the dimeric interface of tubulin. The Ska1 microtubule-binding domain interacts with tubulins using multiple contact sites that allow the Ska complex to bind microtubules in multiple modes. Disrupting either the flexibility or the tubulin contact sites of the Ska1 microtubule-binding domain perturbs normal mitotic progression, explaining the critical role of the Ska complex in maintaining a firm grip on dynamic microtubules.