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We present the results of radio monitoring observations of Sgr A* at 7 mm (i.e. 43 GHz) with the VLBI Exploration of Radio Astrometry (VERA), which is a VLBI array in Japan. VERA provides angular resolution on millisecond scales, resolving structures within 100 Schwarzschild radii of Sgr A* , similar to the Very Large Baseline Array (VLBA). We performed multi-epoch observations of Sgr A* in 2005 - 2008, and started monitoring it again with VERA from 2013 January to trace the current G2 encounter event. Our preliminary results in 2013 show that Sgr A* on mas scales has been in an ordinary state as of August 2013, although some fraction of the G2 cloud already passed the pericenter of Sgr A* in April 2013. We will continue monitoring Sgr A* with VERA and the newly developed KaVA (KVN and VERA Array).