In deep sub-micron technologies, conventional silicon-based transistors are faced main several problems related to the short-channel effects such as power dissipation, subthreshold leakage, and drain-induced barrier lowering (DIBL). Graphene nano-ribbon field-effect transistors (GNRFETs) have become a potential contender as a substitute for traditional silicon-based transistors in next generation nano-electronic devices. They exhibit fantastic properties such as high charge carrier mobility, mean free path of electrons, faster switching, and high ION/IOFF ratio. In order to prove the competences and superiority of these types of transistors, various circuits like full adder (FA) cells, which are the main building block of computational systems must be simulated and studied. This paper presents redesigning various 1-bit FA cells such as Complementary Metal-Oxide-Semiconductor (CMOS), Complementary Pass-Transistor Logic (CPL), Transmission-Gate (TG), Hybrid CMOS (HCMOS), and Transmission Function Adder (TFA) using MOS-GNRFET devices in 16nm technology node. Different HSPICE simulations are performed to obtain propagation delay, average power consumption, power-delay-product (PDP), and energy-delay-product (EDP) of FA cells and are compared with 16nm CMOS predictive technology model (PTM) at different supply voltages. The obtained results indicate that MOS-GNRFET based 1-bit FA cells have better performance than that of Si-CMOS one. The MOS-GNRFET based FA cells improve propagation delay and EDP at least 31.195% and 4.372%, respectively.