The continuous scanning mode in three-dimensional (3D) whole-body PET studies has the advantage of axial sensitivity uniformity over the majority of the axial FOV. However, this scan mode requires large data handling compared to conventional discrete scans. In this work, we have implemented and evaluated a new continuous 3D scan method using 'on-the-fly' Fourier rebinning. In this method, sinograms for the pair of rings are added in real-time into the sinograms of the incremented ring pairs by moving the bed axially one detector width at a time. For an N-ring scanner, 2N--1 sinograms are transferred to a host computer at each bed position and rebinned into direct two-dimensional (2D) sinograms using Fourier rebinning. Phantom and human studies showed that the axial image uniformity is achieved without degrading the axial resolution. This method can minimize the time for off-line data processing and makes the continuous 3D scan more feasible in clinical whole-body studies.