In this paper we have introduced the notion of *-Ricci flow and shown that *-Ricci soliton which was introduced by Kaimakamis and Panagiotidou in 2014 is a self similar soliton of the *-Ricci flow. We have also found the deformation of geometric curvature tensors under *-Ricci flow. In the last two section of the paper, we have found the ...-functional and ω-functional for *-Ricci flow respectively.