Wavefront single-pixel imaging (WSPI) can efficiently capture the amplitude and phase information of an unknown field using a single-pixel detector. However, as the imaging resolution increases, more modulation patterns are required, restricting the imaging speed. Here, we propose a parallel wavefront single-pixel imaging (PWSPI) technique, leveraging grating arrangement and multiplex to establish parallel common-path interferometric detections, for obtaining different parts of the target wavefront simultaneously. Such an approach reduces the number of modulation patterns required and accelerates the imaging speed. Simulations and experimental results show that using four parallel interferometric detections elaborately designed can achieve a fourfold enhancement in the imaging speed while maintaining the imaging quality. We further validate the performance of PWSPI by reconstructing the wavefront of a dragonfly wing, confirming its effectiveness in the application of biological sample imaging. It provides a promising WSPI scheme for a faster acquisition of amplitude and phase information.