Integration of light-trapping features and exploitation of metal nanostructure plasmonic effects are promising approaches for enhancing the power conversion efficiency of organic solar cells. These approaches’ effects on the light absorption enhancement have been widely studied, especially in inorganic devices. While this light-trapping concept can be transferred to organic devices, one has to also consider nanostructure-induced electrical effects on the device performance, due to the fundamental difference in the organic semiconducting material properties compared to their inorganic counterparts. In this contribution, we exemplarily model the electrical properties of organic solar cells with rectangular-grating structures, as compared to planar reference devices. Based on our numeric results, we demonstrate that, beyond an optical absorption enhancement, the device fill factor improves significantly by introducing the grating structures. From the simulations we conclude that enhanced carrier collection efficiency is the main reason for the increased solar cell fill factor. This work contributes towards a more fundamental understanding of the effect of nanostructured electrodes on the electrical properties of organic solar cells.