Fast growth of microtubules is essential for rapid assembly of the microtubule cytoskeleton during cell proliferation and differentiation. XMAP215 belongs to a conserved family of proteins that promote microtubule growth. To determine how XMAP215 accelerates growth, we developed a single-molecule assay to visualize directly XMAP215-GFP interacting with dynamic microtubules. XMAP215 binds free tubulin in a 1:1 complex that interacts with the microtubule lattice and targets the ends by a diffusion-facilitated mechanism. XMAP215 persists at the plus end for many rounds of tubulin subunit addition in a form of "tip tracking." These results show that XMAP215 is a processive polymerase that directly catalyzes the addition of up to 25 tubulin dimers to the growing plus end. Under some circumstances XMAP215 can also catalyze the reverse reaction, namely microtubule shrinkage. The similarities between XMAP215 and formins, actin polymerases, suggest that processive tip tracking is a common mechanism for stimulating the growth of cytoskeletal polymers.