A seamless graphene inverter including graphene nanoribbon field effect transistor (GNRFET) and graphene interconnect is proposed. The seamless structure is suggested to eliminate the ohmic, schottky, and parasitic resistances in the junction of the traditional interconnects with the Gate, Source and Drain of GNRFET. After that, using the circuit models of the graphene devices that are used in the proposed structure, transfer matrix model of the proposed seamless graphene inverter is calculated and extracted. All of the capacitive, inductive and scattering effects are included in the assumed circuit models of the GNRFET-graphene interconnect and consequently in the overall matrix model of the seamless graphene inverter. Elimination of the ohmic, schottky and parasitic resistances causes to improve in the working speed of the proposed inverter. Extraction of the transfer matrix model of the seamless graphene inverter and calculation of its step time response, relative stability and frequency bandwidth confirms this improvement. The advantage of the transfer matrix model of the proposed inverter is that any change in the physical parameters of the graphene nanoribbons that are used in the structure can be included in the model and one can analyze the effect of it in all of the technology nodes. Using the circuit model and the extracted transfer matrix, anyone can evaluates various stability analyses such as Nyquist, Bode and Nichols together with the time-frequency responses of the graphene seamless inverter used in very large scale integrated (VLSI) circuits.