When an adder circuit, which uses less power and operates at a higher speed, is introduced as a fundamental building block, the multiplier, arithmetic and logic unit (ALU), and digital system’s power delay product (PDP) performance can be easily improved. The graphene nanoribbon field effect transistor (GNRFET) used in very large-scale integrated (VLSI) circuits was developed in the submicron regime and offers superior electrical properties to the MOS transistor. This research paper introduces a full-adder circuit containing twelve GNRFETs (12T GF-FA). Calculations have been made about the introduced 12T GF-FA’s power usage, speed, PDP and leakage power. A few of the existing full adders with 8–32 transistors are compared to the performance of the newly proposed 12T GF-FA in terms of power and delay. For this comparison, some conventional full adders with 8–32 transistors have been implemented using 16[Formula: see text]nm technology GNRFETs. The pull-down network of the suggested adder has two stacked GNRFETs. The proposed adder’s current conduction and power consumption are reduced by the use of stacked transistors. According to the simulation results, the PDP of the suggested 12T GF-FA is 73.2–99% lower when compared to other full adders considered state-of-the-art. Additionally, it has been researched and documented how variations in the PVT and GNRFET parameters affect the performance of full-adder circuits. The proposed adder, with its low PDP, is especially suitable for VLSI signal processing applications. The simulation was carried out using the HSPICE simulation tool and the 16[Formula: see text]nm MOS-GNRFET model.