H-polarization, along with E-polarization, indicates the lateral variations of the Earth conductivity, which influence the induced electric field distribution. The coast effect is a typical H-polarization phenomenon that causes local geoelectric field enhancement in coastal areas and significantly affects the geomagnetically induced currents (GIC) distributions in power grids. The influences of H-polarization on geoelectric fields and GIC form the basis for further research on power grid disasters resulting from magnetic storms. In this paper, block and thin-shell models of the coast effect are established, and the electric field distribution in the case of H-polarization is calculated using the finite element method. The results demonstrate the effects of the conductivity, frequency, and distance from the interface of a different conductivity on electric field distortion. Additionally, the relationship between H-polarization and GIC in power grids is investigated, demonstrating that the GIC can be influenced within 100 km in the H-polarization case. The methods and results provide a theoretical basis for GIC risk assessment and development of a control strategy for the power grid.