Microtubules are dynamic cytoskeletal polymers, and their organization and stability are tightly regulated by numerous cellular factors. While regulatory proteins controlling the formation of interphase microtubule arrays and mitotic spindles have been extensively studied, the biochemical mechanisms responsible for generating stable microtubule cores of centrioles and cilia are poorly understood. Here, we used in vitro reconstitution assays to investigate microtubule-stabilizing properties of CSPP1, a centrosome and cilia-associated protein mutated in the neurodevelopmental ciliopathy Joubert syndrome. We found that CSPP1 preferentially binds to polymerizing microtubule ends that grow slowly or undergo growth perturbations and, in this way, resembles microtubule-stabilizing compounds such as taxanes. Fluorescence microscopy and cryo-electron tomography showed that CSPP1 is deposited in the microtubule lumen and inhibits microtubule growth and shortening through two separate domains. CSPP1 also specifically recognizes and stabilizes damaged microtubule lattices. These data help to explain how CSPP1 regulates the elongation and stability of ciliary axonemes and other microtubule-based structures.