The initial kinetochore encounter with a spindle microtubule (kinetochore capture) is one of the rate-limiting steps in establishing proper kinetochore–microtubule interaction during mitosis. Kinetochore capture is facilitated by multiple factors such as microtubule extension in various directions, kinetochore diffusion and microtubule pivoting. In addition, kinetochores generate short microtubules, which subsequently interact with a spindle microtubule. Kinetochore-derived microtubules may facilitate kinetochore capture, but their contribution is elusive. Here we find that Stu1 recruits Stu2 to budding yeast kinetochores, which promotes microtubule generation there. By removing Stu2 specifically from kinetochores, we show that kinetochore-derived microtubules shorten the half-life of non-captured kinetochores from 48–49 to 28–34 seconds. Using computational simulation we find that multiple factors facilitate kinetochore capture, redundantly or synergistically. In particular, kinetochore-derived microtubules play important roles both by making a significant contribution on their own and by synergistically enhancing the effects of KT diffusion and MT pivoting. Our study reveals fundamental mechanisms facilitating the initial kinetochore encounter with spindle microtubules.