The phase-diversity wavefront sensor is a popular means for conducting quantitative wavefront measurements and image restoration from several desired intensity measurements. It has wide applications ranging from adaptive optics in telescopes to optical detection in high-power laser systems. In contrast to traditional phase diversity, we propose a modified version of single-shot quasi-phase-diversity wavefront sensing using a multifocal Fibonacci zone-plate module. The Fibonacci zone plate, designed to generate a specific separation distance between the in-focus and defocused diffraction planes, enables recording multiplanar diffraction patterns at a given position under a single exposure. Thus, this modified wavefront sensing can improve recovery accuracy and realize real-time measurements via a single exposure. In our experiment, a test object fabricated on a chrome plate was measured to verify the validity of the proposed single-shot quasi-phase-diversity wavefront sensing. With the advantages of simple real-time operation and improved measurement accuracy, this technique can be applied to various detection and imaging processes, such as wavefront measurements and image restoration.