Modeling relative permeability in multi-scale rocks and fractured networks has broad applications to understanding oil production and recovery in reservoir formations. Natural porous media are typically composed of two domains; one incorporates macropores, while the other contains micropores. In the literature, numerous theoretic models have been developed based on the series-parallel tubes approach (Mualem, 1976; van Genuchten, 1980) to estimate wetting-phase relative permeability (krw) from pore size distribution or capillary pressure curve. In this study, we, however, invoke concepts from critical path analysis (CPA), a theoretical technique from statistical physics. CPA has been successfully used to model flow and transport in porous media (Hunt, 2001; Ghanbarian-Alavijeh and Hunt, 2012; Hunt et al., 2013; 2014; Ghanbarian et al., 2016; Ghanbarian and Hunt, 2017). We estimate the wetting-phase relative permeability from the measured capillary pressure curve using two methods: (1) critical path analysis (CPA), and (2) series-parallel tubes (vG-M). To evaluate these models, we use 26 experiments from the literature for which capillary pressure and wetting-phase relative permeability data were measured at 500 data point over a wide range of wetting-phase saturation (Sw). Results demonstrate that CPA estimates krw more precisely than vG-M. We show that accurate krw estimation by the CPA-based model needs precise characterization of capillary pressure curve and accurate calculation of the crossover point (Swx) separating the two domains.