Polymer-based pressure sensors play a key role in realizing lightweight and inexpensive wearable devices for healthcare and environmental monitoring systems. Here, conductive core/shell polymer nanofibers composed of poly (vinylidene fluoride-co-hexafluoropropene) (PVDF-HFP)/poly(3,4-ethylenedioxythiophene) (PEDOT) are fabricated using three-dimensional (3D) electrospinning and vapor deposition polymerization methods, and the resulting sponge-like 3D membranes are used to create piezoresistive-type pressure sensors. Interestingly, the PEDOT shell consists of well-dispersed spherical bumps, leading to the formation of a hierarchical conductive surface that enhances the sensitivity to external pressure. The sponge-like 3D mats exhibit a much higher pressure sensitivity than the conventional electrospun 2D mats due to their enhanced porosity and pressure-tunable contact area. Furthermore, large-area, wireless, 16 × 10 multiarray pressure sensors for the spatiotemporal mapping of multiple pressure points and wearable bands for monitoring blood pressure have been fabricated from these 3D mats. To the best of our knowledge, this is the first report of the fabrication of electrospun 3D membranes with nanoscopically engineered fibers that can detect changes in external pressure with high sensitivity. The developed method opens a new route to the mass production of polymer-based pressure sensors with high mechanical durability, which creates additional possibilities for the development of human-machine interfaces.