  The asymptotic Plateau problem asks for the existence of smooth complete
hypersurfaces of constant mean curvature with prescribed asymptotic boundary at
infinity in the hyperbolic space $\mathbb{H}^{n+1}$. The modified mean
curvature flow (MMCF) was firstly introduced by Xiao and the second author a
few years back, and it provides a tool using geometric flow to find such
hypersurfaces with constant mean curvature in $\mathbb{H}^{n+1}$. Similar to
the usual mean curvature flow, the MMCF is the natural negative $L^2$-gradient
flow of the area-volume functional $\mathcal{I}(\Sigma)=A(\Sigma)+\sigma
V(\Sigma)$ associated to a hypersurface $\Sigma$. In this paper, we prove that
the MMCF starting from an entire locally Lipschitz continuous radial graph
exists and stays radially graphic for all time. In general one cannot expect
the convergence of the flow as it can be seen from the flow starting from a
horosphere (whose asymptotic boundary is degenerate to a point).
