Superior electronic properties of graphene make it a substitute candidate for beyond-CMOS nanoelectronics in electronic devices such as the field-effect transistors (FETs), tunnel barriers, and quantum dots. The armchair-edge graphene nanoribbons (AGNRs), which have semiconductor behavior, are used to design the digital circuits. This paper presents a new design of ternary half adder based on graphene nanoribbon FETs (GNRFETs). Because of reducing chip area and integrated circuit (IC) interconnects, ternary value logic is a good alternative to binary logic. Extensive simulations have been performed in Hspice with 15-nm GNRFET technology to investigate the power consumption and delay. Results show that the proposed design is very high-speed in comparison with carbon nanotube FETs (CNTFETs). The proposed ternary half adder based on GNRFET at 0.9V exhibiting a low power-delay-product (PDP) of ~10-20 J, which is a high improvement in comparison with the ternary circuits based on CNTFET, lately proposed in the literature. This proposed ternary half adder can be advantageous in complex arithmetic circuits.