Summary Centrioles are fundamental and evolutionarily conserved microtubule-based organelles whose assembly is characterized by microtubule growth rates that are orders of magnitude slower than those of cytoplasmic microtubules. Several centriolar proteins can interact with tubulin or microtubules, but how they ensure the exceptionally slow growth of centriolar microtubules has remained mysterious. Here, we bring together crystallographic, biophysical, and reconstitution assays to demonstrate that the human centriolar protein CPAP (SAS-4 in worms and flies) binds and “caps” microtubule plus ends by associating with a site of β-tubulin engaged in longitudinal tubulin-tubulin interactions. Strikingly, we uncover that CPAP activity dampens microtubule growth and stabilizes microtubules by inhibiting catastrophes and promoting rescues. We further establish that the capping function of CPAP is important to limit growth of centriolar microtubules in cells. Our results suggest that CPAP acts as a molecular lid that ensures slow assembly of centriolar microtubules and, thereby, contributes to organelle length control., Highlights • CPAP's PN2-3 domain binds to an exposed site on β-tubulin at microtubule plus ends • CPAP tracks and caps microtubule plus ends in vitro • CPAP dampens microtubule growth in vitro • The capping function of CPAP limits centriolar microtubule growth in human cells, The mechanisms ensuring the extremely slow growth of centriolar microtubules remain elusive. Sharma, Aher, Dynes et al. demonstrate that human CPAP acts as a molecular lid that caps microtubule plus ends and dampens their elongation, thus contributing to centriole length control by ensuring slow processive assembly of centriolar microtubules.