[4,5], arithmetic circuits [6] and so on, taking advantages of its unique attributes. However, among these circuits arithmetic circuits could be more interesting, due to their vast range of applications. Many VLSI systems such as microprocessors, DSP architectures and nano-micro systems [7,8,9] have arithmetic unit, which is also included in their critical path. One of the most important and basic arithmetic units is Full Adder, which could be the basic structure of many complex arithmetic systems and as a results its performance directly affects the performance of the whole system. Therefore, it is necessary to design novel Full Adder structures with higher performance and lower power consumption, based on the emerging nano technologies. In this paper a new energy-efficient 1-bit Full Adder cell is proposed, which takes advantage of CNFET devices and high density Carbon Nanotube Capacitors (CNCAP) [10]. The proposed circuit is also compared with the classical and state-of-the-art CMOS and CNFET-based Full Adders, with different styles, which are briefly introduced in this section.