Stretchable fiber and yarn triboelectric nanogenerator are sought for such applications as wearable sensing system such as cloth communication devices, electronic textiles, and robotic sensory skin. Unfortunately, previously reported triboelectric fiber and yarn are difficult to have stretchable property. We introduce here a new type of stretchable and weavable triboelectric fibers with microdiameter dimensions. The stretchable triboelectric fibers can be reversibly stretched up to 50% in tensile direction while generating voltage output proportional to the applied tensile strain. The reversible distance change induced by the Poisson's ratio difference between the core fiber (silver-coated nylon/polyurethane) and the shell (wrinkled polyvinylidene fluoride-co-trifluoroethylene/carbon nanotube layer) during tensile deformation is the key working principle for electrical generation. Owing to exceptional structural stability, the stretchable triboelectric fibers show high performance retention after 10,000 times repeated stretching/releasing cycle. Furthermore, the stretchable triboelectric fibers are mechanically strong to be woven into a commercial textile for textile based sensors, which can detect magnitude as well as direction of the motion.