A modified helium gas closed cycle cryogenic system has been used to measure the zero field cooling levitation force relaxation as a function of temperature (40–85 K) for three different sizes of YBCO superconducting sample. The time range in our relaxation measurements was from 3 s to 1000 s. A linear logarithmic decay of the levitation forces with time was observed. It was found that the levitation force might decrease more than forty percent in our measured interval. It was also found that the higher temperature and the smaller size the superconductor we have, the faster the levitation force it decays, as one would expected.