A discrete conformality for hyperbolic polyhedral surfaces is introduced
in this paper. This discrete conformality is shown to be computable.
It is proved that each hyperbolic polyhedral metric on a closed surface is discrete
conformal to a unique hyperbolic polyhedral metric with a given discrete
curvature satisfying Gauss-Bonnet formula. Furthermore, the hyperbolic polyhedral
metric with given curvature can be obtained using a discrete Yamabe
flow with surgery. In particular, each hyperbolic polyhedral metric on a closed
surface with negative Euler characteristic is discrete conformal to a unique
hyperbolic metric.