  We show that the results in \cite{Ge-Jiang1} are still true in hyperbolic
background geometry setting, that is, the solution to Chow-Luo's combinatorial
Ricci flow can always be extended to a solution that exists for all time,
furthermore, the extended solution converges exponentially fast if and only if
there exists a metric with zero curvature. We also give some results about the
range of discrete Gaussian curvatures, which generalize Andreev-Thurston's
theorem to some extent.
