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