Abstract Realistic random networks of carbon nanotubes (CNTs) were simulated by the noble hybrid method combining Monte Carlo and SPICE simulations. Near the percolation threshold, the electrical characteristics of networks are strongly affected by the contacts among nanotubes. The nonlinear electrical junctions in the CNT network were modeled by suitable SPICE models and simulated using our hybrid simulation method. We successfully described the morphological percolation threshold, and the critical density was determined as a function of normalized length. The effects of electrical junctions on the scaling of the sheet conductance were investigated.