The magnetic relaxation and critical current density have been measured on
a MgB2 thin film in a wide region of temperature with magnetic field up to
8 T. The irreversibility line has also been determined. It is found that th
e relaxation rate has a very weak temperature dependence below 1/2T(c). sho
wing a clear residual relaxation rate at 0 K, which cannot be easily explai
ned as due to thermally activated flux creep. Furthermore, the relaxation r
ate has a strong field dependence. The flux dynamics of thin films is very
similar to that of high-pressure synthesized bulks although the relaxation
rate in thin film is systematically higher than that of a bulk sample. All
the results here together with those from bulk samples suggest that the flu
x dynamics may be dominated by quantum effects, such as quantum fluctuation
and tunneling.