For proper chromosome segregation, sister kinetochores must interact with microtubules from opposite spindle poles; this is called bi-orientation. To establish bi-orientation prior to chromosome segregation, any aberrant kinetochore–microtubule interaction must be resolved (error correction) by Aurora B kinase that phosphorylates outer kinetochore components. Aurora B differentially regulates kinetochore attachment to the microtubule plus end and its lateral side (end-on and lateral attachment). However, it is still unknown how kinetochore–microtubule interaction is turned over during error correction. Here we reconstituted the kinetochore–microtubule interface in vitro by attaching Ndc80 protein complexes (Ndc80Cs) to a nanobead that mimics the inner kinetochore. The Ndc80C–nanobeads recapitulated in vitro the lateral and end-on attachments of authentic kinetochores on dynamic microtubules loaded with the Dam1 complex. Using this system, we provide evidence that error correction is driven by direct competition for a kinetochore between the end-on attachment to one microtubule and the lateral attachment to another. We validated this competition-based error correction, using mathematical modelling and live-cell imaging. Our study reveals a fundamental mechanism of error correction, which contributes to efficient establishment of bi-orientation.