An efficient method to estimate the absolute permeability of three-dimensional percolation networks was proposed. It uses a Kozeny-Carman relationship in the form of a scaling law to relate the network permeability to its hydraulic characteristic length. This characteristic length was determined at the network percolation threshold using a three-dimensional extension of the Hoshen-Kopelman algorithm. For developing the scaling laws, the network permeability was calculated by solving the Kirchoff's law for all sample spanning clusters that had been identified by the three-dimensional version of the Hoshen-Kopelman algorithm. The method was tested with simple cubic site-bond network models with and without spatial correlations. The universality of the exponents in the scaling laws were also investigated. It was shown that, once the scaling law has been derived, the permeability value can be estimated 3-9 times faster using the present method.