  For triangulated surfaces locally embedded in the standard hyperbolic space,
we introduce combinatorial Calabi flow as the negative gradient flow of
combinatorial Calabi energy. We prove that the flow produces solutions which
converge to ZCCP-metric (zero curvature circle packing metric) if the initial
energy is small enough. Assuming the curvature has a uniform upper bound less
than $2\pi$, we prove that combinatorial Calabi flow exists for all time.
Moreover, it converges to ZCCP-metric if and only if ZCCP-metric exists.
