This paper presents a novel inexact full adder based on carbon nanotube field-effect transistors (CNTFET) for approximate computations, which has soared in popularity especially for image processing applications. The proposed design generates the output carry without error. Therefore, the propagation of incorrect value to higher bit positions is avoided. It has the least relative error distance (Relative ED) compared to other approximate full adders reported in the literature. Practical simulations by using MATLAB demonstrate higher peak signal to noise ratio (PSNR) and image quality for motion detector image processing application. HSPICE simulations also confirm the effciency of the proposed design. Moreover, area occupation is investigated by using electric tool. Power consumption, delay, area and ED are important evaluating factors in this subject. Comparisons are made by a comprehensive parameter (PDAEDP), based on which the new design has 23.8%, 41.5%, 70.5%, 78% and 83.6% higher performance than TGA1, TGA2, AXA1, AXA2 and AXA3, respectively.