Recently, flexible strain sensors with large stretchability, high sensitivity and excellent stability have been widely concerned owing to their potential applications in wearable electronic devices. However, the challenge of narrow sensing range still remains for strain sensors with high performance. In this paper, we proposed a facile, cost-effective and scalable technology to manufacture the carbon nanotubes (CNTs)/thermoplastic polyurethane (TPU) fibrous strain sensor with aligned wave-like structure. Through electrospinning technique, we prepared an aligned TPU fibrous mat, then used a simple and effective assembly approach to induce CNTs to wrap TPU fibrous mat through ultrasonication. The sensing properties of CNTs/TPU mats in vertical and parallel directions were investigated, respectively. The sensing behaviors of the two sensors both agreed well with the tunneling theory. Compared with the random CNTs/TPU mats and parallel direction sample, the aligned CNTs/TPU fibrous mats in vertical direction possessed an ultra-high stretchability (900%) and excellent durability (10,000 cycles at the strain of 200%). An ultra-low detection limit (0.5%) and fast response time of 70 ms were also achieved, exhibiting a favorable sensitivity. The generation of the wave-like structure and the joints structure in the designed conductive network, which could affect the evolution of the conductive paths subsequently, led to these excellent sensing performances. The CNTs/TPU mats strain sensor was then assembled to monitor both subtle human motions, like cheek bulging and phonation; and vigorous human motions, like leg squatting and elbow bending, both showing excellent sensing performances. The present paper provides a good candidate for potential applications as artificial skins, human-activity monitoring and personal healthcare.