Pressure sensors have been widely used in electronic wearable devices and medical devices to detect tiny physical movements and mechanical deformation. However, it remains a challenge to fabricate desirable, comfortable wearing, and highly sensitive as well as fast responsive sensors to capture human body physiological signs. Here, a new capacitive flexible pressure sensor that is likely to solve this problem was constructed using thermoplastic polyurethane elastomer rubber (TPU) electrospinning nanofiber membranes as a stretchable substrate with the incorporation of silver nanowires (AgNWs) to build a composite dielectric layer. In addition, carbon nanotubes (CNTs) were painted on the TPU membranes as flexible electrodes by screen printing to maintain the flexibility and breathability of the sensors. The flexible pressure sensor could detect tiny body signs; fairly small physical presses and mechanical deformation based on the variation in capacitance due to the synergistic effects of microstructure and easily altered composite permittivity of AgNW/TPU composite dielectric layers. The resultant sensors exhibited high sensitivity (7.24 kPa⁻¹ within the range of 9.0 × 10⁻³ ~ 0.98 kPa), low detection limit (9.24 Pa), and remarkable breathability as well as fast responsiveness (<55 ms). Moreover, both continuously pressing/releasing cycle over 1000 s and bending over 1000 times did not impair the sensitivity, stability, and durability of this flexible pressure sensor. This proposed strategy combining the elastomer nanofiber membrane and AgNW dopant demonstrates a cost-effective and scalable fabrication of capacitive pressure sensors as a promising application in electronic skins and wearable devices.