We report the results of μSR measurement of the re-entrant spin-glass thiospinel CuCrZrS4. We have observed a relatively small enhancement of the relaxation rate at TC∼60K but no oscillations in the time spectra in the first magnetic phase between TC and Tf∼7K, suggesting that the first magnetic phase is not a long-range ordering state. A fast depolarization component in ZF-μSR appears around 40K and develops accompanied by the rapid increase of its relaxation rate with decreasing temperature down to Tf. The fast depolarization component is interpreted as the signature of the magnetic correlation attributed to the re-entrant spin-glass behavior. At all the measured temperatures, there remain relaxations even at high magnetic fields, revealing a dynamical local field due to strong magnetic correlations.