Graphene research has attracted enormous attention in the past few years. The handling of graphene sheets, however, has become one of the major bottlenecks in this field, especially in the development of practical devices. Here we report the investigation of large-scale deposition of graphene sheets with dielectrophoresis, a simple electrical approach using alternating current (AC) signals. For comparison purposes, we also perform the deposition of semiconducting single-walled carbon nanotubes (s-SWNTs) with the same technique. Images from scanning electron microscopy (SEM) show that the graphene flakes are successfully deposited over the "teeth"-shaped electrodes. However, the graphene deposition has a lower yield compared with the s-SWNT deposition. Both the graphene and s-SWNT based devices are subject to water rinsing after the deposition process. The current-voltage (I-V) plots before and after the rinsing steps for both devices demonstrate that the surfactants wrapping the nanomaterials can be removed by the running de-ionized water; and better electrical contacts can be formed at the interfaces of nanomaterials and electrodes. In order to further study the electrical characteristics of the deposited graphene and s-SWNTs, a standard Ag/AgCl electrode is introduced to both devices, serving as a top liquid-gate terminal. The output characteristics of both devices exhibit p-type field-effect transistor behavior. The s-SWNT based device possesses better field-effect characteristics, whereas the graphene based device has higher conductivity and more apparent metallic properties. The reported research presents an effective approach in large-scale deposition of graphene and it has great potential of paving the way for future graphene-related research and applications, especially in nanoelectronics and sensors.