Coronary atherosclerotic plaque rupture is the main cause of myocardial infarction and the leading killer in the US. Inflammation is a known bio-marker of plaque vulnerability and can be assessed non-invasively using fluorodeoxyglucose-positron emission tomography imaging (FDG-PET). However, cardiac and respiratory motion of the heart makes PET detection of coronary plaque very challenging. Fat surrounding coronary arteries allows the use of MRI to track plaque motion during simultaneous PET-MR examination. In this study, we proposed and assessed the performance of a fat-MR based coronary motion correction technique for improved FDG-PET coronary plaque imaging in simultaneous PET-MR. The proposed methods were evaluated in a realistic four-dimensional PET-MR simulation study obtained by combining patient water-fat separated MRI and XCAT anthropomorphic phantom. Five small lesions were digitally inserted inside the patients coronary vessels to mimic coronary atherosclerotic plaques. The heart of the XCAT phantom was digitally replaced with the patient's heart. Motion-dependent activity distributions, attenuation maps, and fat-MR volumes of the heart, were generated using the XCAT cardiac and respiratory motion fields. A full Monte Carlo simulation using Siemens mMR's geometry was performed for each motion phase. Cardiac/respiratory motion fields were estimated using non-rigid registration of the transformed fat-MR volumes and incorporated directly into the system matrix of PET reconstruction along with motion-dependent attenuation maps. The proposed motion correction method was compared to conventional PET reconstruction techniques such as no motion correction, cardiac gating, and dual cardiac-respiratory gating. Compared to uncorrected reconstructions, fat-MR based motion compensation yielded an average improvement of plaque-to-background contrast of 29.6%, 43.7%, 57.2%, and 70.6% for true plaque-to-blood ratios of 10, 15, 20 and 25:1, respectively. Channelized Hotelling observer (CHO) signal-to-noise ratio (SNR) was used to quantify plaque detectability. CHO-SNR improvement ranged from 105% to 128% for fat-MR-based motion correction as compared to no motion correction. Likewise, CHO-SNR improvement ranged from 348% to 396% as compared to both cardiac and dual cardiac-respiratory gating approaches. Based on this study, our approach, a fat-MR based motion correction for coronary plaque PET imaging using simultaneous PET-MR, offers great potential for clinical practice. The ultimate performance and limitation of our approach, however, must be fully evaluated in patient studies.