The presence of motion effects during PET acquisition degrades the reconstructed image quality. Recently, a data-driven motion estimation and correction algorithm based on PET/CT scanners employing Silicon Photomultipliers (SiPM) detectors is proposed. The algorithm is able to capture motion effects in all three directions at 1-second temporal resolution which is highly effective for respiratory and body motion monitoring and correction. In this study, we extend a previously developed event-by-event list-mode reconstruction framework to handle the datasets and motion vectors derived from the algorithm to achieve 3-dimensional (3D) continuous motion correction. The NEMA phantom and 74 patient datasets acquired on Siemens Biograph Vision PET/CT scanners are included for the performance evaluation of the reconstruction framework. Preliminary results demonstrated the effectiveness of the algorithm and benefits of conducting 3D motion correction in certain cases, although 1D correction in the axial direction might be sufficient for patients with primary superior-inferior motion. In conclusion, the proposed list-mode reconstruction framework is able to effectively correct 3D and 1D rigid motion in cardiac PET.