Stretchable yarn/fiber electronics with conductive features are optimal components for different wearable devices. This paper presents the construction of coil structure-based carbon nanotube (CNT)/polymer fibers with adjustable piezoresistivity. The composite unit fiber is prepared by wrapping a conductive carbon CNT sheath onto an elastic spandex core. Owing to the helical coil structure, the resultant CNT/polymer composite fibers are highly stretchable (up to approximately 300%) without a noticeable electrical breakdown. More specifically, based on the difference in the coil index (which is the ratio of the coil diameter to the diameter of the fiber within the coil) according to the polymeric core fiber (spandex or nylon), the composite fiber can be used for two different applications (i.e., as strain sensors or supercapacitors), which are presented in this paper. The coiled CNT/spandex composite fiber sensor responds sensitively to tensile strain. The coiled CNT/nylon composite fiber can be employed as an elastic supercapacitor with excellent capacitance retention at 300% strain.