Vugular carbonate rocks have a complicated flow behavior because of their multimodal porosity system, with different interconnectivity at the pore scale. In this study, a new hybrid algorithm to reconstruct a bimodal vugular porous medium is introduced by coupling the pore‐network modeling approach (i.e., stochastic) with the image‐based network technique (i.e., process‐based). This work implements image‐processing techniques to generate a lattice‐based network of secondary porosity (i.e., vugs) on top of an initial pore‐network model at the pore scale. The resulting multiscale model is designed to preserve vug‐to‐vug and vug‐to‐pore connectivity of overlapping vugs. Modifying the effective conductance of the overlapped vugs enables the calculation of permeability of the dual‐porosity network by applying mass conservation and the Poiseuille law. The method is validated on samples from an Iranian carbonate formation. The matrix micropores obtained from the mercury‐intrusion laboratory measurements are statistically reconstructed by a Nelder‐Mead optimization algorithm. Our results show that during the addition of vugs into a network, the absolute permeability of the network increases monotonically with rising porosity before vug percolation. However, once vuggy pores percolate, the absolute permeability of the network increases tremendously. Moreover, the availability of vugs makes the network structure more complex as determined by the off‐diagonal complexity measure. The results of this study help in understanding the behavior of vuggy formations observed in carbonate reservoirs.