Flexible and wearable pressure sensors have attracted extensive attention in domains, such as electronic skin, medical monitoring and human-machine interaction. However, developing a pressure sensor with high sensitivity, mechanical stability and a wide detection range remains a huge challenge. In this work, a flexible capacitive pressure sensor, based on a Ti3C2Tx (MXene)/polyvinyl pyrrolidone (PVP) composite nanofiber membrane (CNM), prepared via an efficient electrospinning process, is presented. The experimental results show that even a small mass fraction of MXene can effectively decrease the compression modulus of the PVP nanofiber membrane, thus enhancing the sensing performance. Specifically, the sensor based on (0.1 wt% MXene)/PVP CNM has a high sensitivity (0.5 kPa(-1) at 0-1.5 kPa), a fast response/recovery time (45/45 ms), a wide pressure detection range (0-200 kPa), a low detection limit (similar to 9 Pa) and an excellent mechanical stability (8000 cycles). Due to its superior performance, the sensor can monitor subtle changes in human physiology and other signals, such as pulse, respiration, human joint motions and airflow. In addition, a 4 x 4 sensor array is fabricated that can accurately map the shape and position of objects with good resolution. The high-performance flexible pressure sensor, as developed in this work, shows good application prospects in advanced human-computer interface systems.