Flexible pressure sensors based on paper have attracted considerable attention owing to their good performance, low cost, and environmental friendliness. However, effectively expanding the detection range of paper-based sensors with high sensitivities is still a challenge. Herein, we present a paper-based resistive pressure sensor with a sandwich structure consisting of two electrodes and three sensing layers. The silver nanowires were dispersed deposited on a filter paper substrate using the vacuum filtration coating method to prepare the electrode. And the sensing layer was fabricated by coating carbon nanotubes onto a mulberry paper substrate. Waterborne polyurethane was introduced in the process of preparing the sensing layers to enhance the strength of the interface between the carbon nanotubes and the mulberry paper substrate. Therefore, the designed sensor exhibits a good sensing performance by virtue of the rational structure design and proper material selection. Specifically, the rough surfaces of the sensing layers, porous conductive network of silver nanowires on the electrodes, and the multilayer stacked structure of the sensor collaboratively increase the change in the surface contact area under a pressure load, which improves the sensitivity and extends the sensing range simultaneously. Consequently, the designed sensor exhibits a high sensitivity (up to 6.26 kPa−1), wide measurement range (1000 kPa), low detection limit (~1 Pa), and excellent stability (1000 cycles). All these advantages guarantee that the sensor has potential for applications in smart wearable devices and the Internet of Things.