In this work, we propose the design of a flexoelectric sensor, which can measure sound-pressure gradient directly. It is found that the sensitivity of sound-pressure gradient of the flexoelectric sensor has a wide band for low working frequencies. Our theoretical and experimental results indicate that the position of sound sources can be predicted based on the measured sound-pressure gradients of three flexoelectric sensors, which are perpendicular to each other. Moreover, different from the previous design for a piezoelectric sensor array, only three flexoelectric sensors are needed to determine the orientation of sound sources. The flexoelectric sensor proposed here may provide an alternative way for the pressure-gradient measurement.