This article presents novel high speed and low power full adder cells based on carbon nanotube field effect transistor (CNFET). Four full adder cells are proposed in this article. First one (named CN9P4G) and second one (CN9P8GBUFF) utilizes 13 and 17 CNFETs respectively. Third design that we named CN10PFS uses only 10 transistors and is full swing. Finally, CN8P10G uses 18 transistors and divided into two modules, causing Sum and Cout signals are produced in a parallel manner. All inputs have been used straight, without inverting. These designs also used the special feature of CNFET that is controlling the threshold voltage by adjusting the diameters of CNFETs to achieve the best performance and right voltage levels. All simulation performed using Synopsys HSPICE software and the proposed designs are compared to other classical and modern CMOS and CNFET-based full adder cells in terms of delay, power consumption and power delay product.