Airflow sensor is a crucial component in many engineering settings, such as sustainable energy utilization, environmental monitoring, weather forecasting, and aerospace engineering. However, few developed airflow sensors can exhibit decent sensing capability towards ultra-low-speed airflows owing to the performance limitations of sensing elements. In this work, we adopt a near-field electrospinning method to direct-write highly aligned poly(vinylidene-trifluoroethylene) (P(VDF-TrFE)) nano/micro fibers onto a flexible substrate with pre-designed interdigital electrodes to form a piezoelectric sensing film (PSF); the fabricated PSF is then used for airflow sensing application. We theoretically derive the output voltage of a single P(VDF-TrFE) fiber on the PSF under airflow loading, and numerically elucidate the dependency of output voltage on device and experimental parameters. Experimental results show that the lower detection limit of our airflow sensor can be as low as 0.3 m/s with the sensitivity of up to 15 mV/(m/s), which has been hardly accomplished in previous piezoelectric airflow sensors. This study not only presents a high-performance piezoelectric nano/micro-fiber-integrated airflow sensor, but also provides a universal electromechanical analysis method for piezoelectric fiber-based flexible electronics under pressure loading.