Resistive transitions of the new superconductor MgB2 are carried out under magnetic fields from 0 to 8 T.It is found that the irreversibility field Hirr(T) and the upper critical field Hc2(T) obtained are very close tothose determined in the magnetic measurements. By using the Arrhenius activation law p＝poexp(- U/kB T), theactivation barrier U has been determined by the low dissipation part of R(T) curves. It is found that U 》 kBTmanifesting a very weak thermal activation and thermal fluctuation effect. This may further indicate that theflux dynamics near Hirr(T) is induced by strong quantum fluctuation and tunnelling of vortices.