Many practical applications require flexible high-sensitivity pressure sensors. However, such sensors are difficult to achieve using conventional materials. Engineering the morphology of the electrodes and the topography of the dielectrics has been demonstrated to be effective in boosting the sensing performance of capacitive pressure sensors. In this study, a flexible capacitive pressure sensor with high sensitivity was fabricated by using three-dimensional vertical graphene (VG) as the electrode and micro-pyramidal polydimethylsiloxane (PDMS) as the dielectric layer. The engineering of the VG morphology, size, and interval of the micro-pyramids in the PDMS dielectric layer significantly boosted the sensor sensitivity. As a result, the sensors demonstrated an exceptional sensitivity of up to 6.04 kPa⁻¹ in the pressure range of 0–1 kPa, and 0.69 kPa⁻¹ under 1–10 kPa. Finite element analysis revealed that the micro-pyramid structure in the dielectric layer generated a significant deformation effect under pressure, thereby ameliorating the sensing properties. Finally, the sensor was used to monitor finger joint movement, knee motion, facial expression, and pressure distribution. The results indicate that the sensor exhibits great potential in various applications, including human motion detection and human-machine interaction.