We have measured the temperature dependence of magnetic relaxation and critical current in an YBaCuO single crystal. Unusually strong time-logarithmic magnetic relaxation is observed. The relaxation rate increases initially with temperature, peaks at ≅25 K and slows down at higher temperatures. The results, interpreted with a thermally activated flux model, yield a low-temperature pinning energy U0≅0.02 eV. This low pinning energy results in an unusually rapid decrease of the critical current as temperature is increased.