Recent development of PET/MR hybrid imaging has provided simultaneous acquisition of anatomical/functional information from MR imaging and molecular/metabolic information from PET imaging. The combinations of a variety of functional imaging from both PET and MRI are expected to improve diagnostic accuracies and management of treatment in oncology patients. This article reviews the history and background theory behind the development of PET/MR system as well as the actual procedure of patient set-up and image acquisition with the PET/MR system for oncology patients. Also described are dedicated MR sequences and PET reconstruction, the indication of health insurance, and the method of image reading and evaluation. Finally, the roles of FDGPET/ MR imaging in clinical practice of oncology patients were reviewed and discussed in each area of head and neck, lung, abdomen and MSK. Our recent research of voxel-based direct comparison between SUV of FDG-PET and ADC of DWI-MR was also mentioned. In summary, the multiparametric molecular imaging with PET/MR is a new diagnostic tool for oncology, and could provide more anatomical/functional information than the conventional PET/CT. Although there remain some technical issues to be solved, the PET/MR system has a potential to replace PET/CT system in future.