Cardiac and respiratory motion artefacts in PET imaging have been traditionally resolved by acquiring the data in gated mode. However, gated PET images are usually characterized by high noise content due to their low photon statistics. In this paper, we present a novel 4D model for the PET imaging system, which can incorporate motion information to generate a motion-free image with all acquired data. A computer simulation and a phantom study were conducted to test the performance of this approach. The computer simulation was based on a digital phantom that was continuously scaled during data acquisition. The phantom study, on the other hand, used two spheres in a tank of water, all of which were filled with ¹⁸F water. One of the spheres was stationary while the other moved in a sinusoidal fashion to simulate tumour motion in the thorax. Data were acquired using both 4D CT and gated PET. Motion information was derived from the 4D CT images and then used in the 4D PET model. Both studies showed that this 4D PET model had a good motion-compensating capability. In the phantom study, this approach reduced quantification error of the radioactivity concentration by 95% when compared to a corresponding static acquisition, while signal-to-noise ratio was improved by 210% when compared to a corresponding gated image.