Non-thermal TeV gamma -ray emission within multi-pc scale has been observed from the center region of our galaxy. We argue that these gamma -rays are the result of a transient activity of the massive black hole Sgr A^* which resides at the Galactic center. About thousands of years ago, the black hole may have experienced an active phase by capturing a red giant star and forming an accretion disk, temporarily behaving like an active galactic nuclear. A powerful jet, which contains plenty of high speed protons, was launched during the process. These runaway protons interact with the dense ambient medium, producing TeV gamma -ray emission through the \pi^o-decay process. We show that the total energy deposited in this way is large enough to account for observations. The diffusion length of protons is also consistent with the observed size of the TeV source.