The complex conductivity method is frequently used in hydro-/petro-/environmental geophysics, and considered to be a promising tool for characterizing and quantifying the properties of subsurface rocks, sediments and soils. We report a study on the complex conductivity characteristics of porous media containing gas hydrates through numerical modelling. The effects of the hydrate saturation, pore-water salinity and micro-distribution mode were studied, and hydrate-saturation evaluation correlations based on complex conductivity parameters were developed. A pore-scale numerical approach for developing the finite-element based models for hydrate-bearing porous media is proposed and a two-dimensional (2D) model is built to compute the complex conductivity responses of porous media under various conditions. We demonstrate that the simple 2D model can capture the dominant characteristics of the complex conductivity of hydrate-bearing porous media within the frequency range related to the induced polarization. The in-phase conductivity, quadrature conductivity and effective dielectric constant can be correlated with the saturation based on a power law in the log-log space, by which the hydrate-saturation evaluation models can be derived. A constant saturation exponent of the power-law correlation between the hydrate saturation and quadrature conductivity can be obtained when the pore-water conductivity exceeds 1.0 S/m. This is highly desirable in the hydrate-saturation models due to the variations of the pore-water conductivity in the processes of hydrate formation and dissociation. Within the framework of the complex conductivity analysis, the micro-distribution modes of hydrates in porous media can be categorized into two types. These are the fluid-suspending mode and grain-attaching mode. The in-phase conductivity exhibits significant variations under the same saturation and salinity but different micro-distribution modes, which can be attributed to the change in the tortuosity of the electrical conduction paths in the void space of porous media.