We have performed monitoring observations of the 3-mm flux density toward the Galactic Center compact radio source Sgr A* with the Australia Telescope Compact Array since 2005 October . Careful calibrations of both elevation-dependent and time-dependent gains have enabled us to establish the variability behavior of Sgr A* . Sgr A* appeared to undergo a high and stable state in 2006 June session , and a low and variable state in 2006 August session . We report the results , with emphasis on two detected intra-day variation events during its low states . One is on 2006 August 12 when Sgr A* exhibited a 33 % fractional variation in about 2.5 hr . The other is on 2006 August 13 when two peaks separated by about 4 hr , with a maximum variation of 21 % within 2 hr , were seen . The observed short timescale variations are discussed in light of two possible scenarios , i.e. , the expanding plasmon model and the sub-Keplerian orbiting hot spot model . The fitting results indicate that for the adiabatically expanding plasmon model , the synchrotron cooling can not be ignored , and a minimum mass-loss rate of 9.7 \times 10 ^ { -10 } M _ { \odot } yr ^ { -1 } is obtained based on parameters derived for this modified expanding plasmon model . Simultaneous multi-wavelength observation is crucial to our understanding the physical origin of rapid radio variability in Sgr A* .