We have performed monitoring observations of the flux density toward the Galactic center compact radio source, Sagittarius A* (Sgr A*), which is a supermassive black hole, from 1996 to 2005 using the Nobeyama Millimeter Array of the Nobeyama Radio Observatory, Japan. These monitoring observations of Sgr A* were carried out in the 3-and 2-mm (100 and 140 GHz) bands, and we have detected several flares of Sgr A*. We found intraday variation of Sgr A* in the 2000 March flare. The twofold increase timescale is estimated to be about 1.5 hr at 140 GHz. This intraday variability suggests that the physical size of the flare-emitting region is compact on a scale at or below about 12 AU (≈150 RS; Schwarzschild radius). On the other hand, clear evidence of long-term periodic variability was not found from a periodicity analysis of our current millimeter data set. this period, we detected no significant mm-flare in unfavorable weather conditions.Reference [20] reported the presence of a 106 day periodicity in the centimeter flux variability of Sgr A* from the analysis of data observed with the VLA over 20 years. We showed that the millimeter light curve exhibits distinct high and low activity states, by folding our NMA data with this period of 106 days [14]. These results may indicate a quasi-periodic flux variability of Sgr A* at mm-wavelengths. Then we carried out a periodicity analysis using the Lomb-Scargle periodogram method for our NMA data at 3-mm [18]. However, no significant peak in the normalized power spectra is found for the entire 3-mm data set. For the subset of these data after 2000, the power spectra has a peak at 0.0101d −1 corresponding to a ~99 day period, with a significance level of 0.37 (false alarm probability). Thus, from the analysis, this periodicity is not significant for our data [18]. Our current sampling is probably insufficient to detect a periodicity, if we consider possible fluctuations in the period, as indicated in recent analysis of VLA cm-data [21].