In recent years, graphene nanomesh (GNM), a material with high flexibility and tunable electronic properties, has attracted considerable attention from researchers due to its wide applications in the fields of nanoscience and nanotechnology. Herein, we have processed large-area, uniform arrays of rectangular graphene nanomesh (r-GNM) and circular graphene nanomesh (c-GNM) with different neck widths by electron beam lithography (EBL). The electronic properties of those high-quality GNM samples have been characterized systematically. Electrical measurements illustrated that top-gated field effect transistors with different neck widths of the GNM possessed different Ion/Ioff ratios. In particular, the devices based on r-GNM with a neck width of 30 nm were found to possess the largest Ion/Ioff ratio of ~ 100, and the band gap of the r-GNM was estimated to be 0.23 eV, which, to the best of authors’ knowledge, is the highest value for graphene ribbons or a GNM with a neck width under 30 nm. Furthermore, the terahertz response of large-area r-GNM devices based on the photoconductive effect was estimated to be 10 mA/W at room temperature. We also explored the practical application of terahertz imaging, showing that the devices can be used in a feasible setting with a response time < 20 ms; this enables accurate and fast imaging of macroscopic samples.