The development of capacitive pressure sensors with low cost, high sensitivity and facile fabrication techniques is desirable for flexible electronics and wearable devices. In this project, a highly sensitive and flexible capacitive pressure sensor was fabricated by sandwiching a porous PAP sponge dielectric layer between two copper electrodes. The porous PAP sponge dielectric layer was fabricated by introducing highly conductive silver nanowires (AgNWs) into the PDMS sponge with 100% sucrose as a template and with a layer of polydimethylsiloxane (PDMS) film coating the surface. The sensitivity of the PAP sponge capacitive pressure sensor was optimized by increasing the load amount of AgNWs. Experimental results demonstrated that when the load amount of AgNWs increased to 150 mg in the PAP sponge, the sensitivity of the sensor was the highest in the low-pressure range of 0–1 kPa, reaching 0.62 kPa−1. At this point, the tensile strength and elongation of sponge were 1.425 MPa and 156.38%, respectively. In addition, the specific surface area of PAP sponge reached 2.0 cm2/g in the range of 0–10 nm pore size, and showed excellent waterproof performance with high elasticity, low hysteresis, light weight, and low density. Furthermore, as an application demonstration, ~110 LED lights were shown to light up when pressed onto the optimized sensor. Hence, this novel porous PAP-sponge-based capacitive pressure sensor has a wide range of potential applications in the field of wearable electronics.