Respiratory motion causes misalignments between positron emission tomography (PET) and magnetic resonance (MR)-derived attenuation maps (µ-maps) in addition to artifacts on both PET and MR images in simultaneous PET/MRI for organs such as liver that can experience motion of several centimeters. To address this problem, we developed an efficient MR-based attenuation correction (MRAC) method to generate phase-matched µ-maps for quiescent period PET (PET) in abdominal PET/MRI. MRAC data was acquired with CIRcular Cartesian UnderSampling (CIRCUS) sampling during 100 s in free-breathing as an accelerated data acquisition strategy for phase-matched MRAC (MRAC). For comparison, MRAC data with raster (Default) k-space sampling was also acquired during 100 s in free-breathing (MRAC), and used to evaluate MRAC as well as un-matched MRAC (MRAC) that was un-gated. We purposefully oversampled the MRAC data to ensure we had enough information to capture all respiratory phases to make this comparison as robust as possible. The proposed MRAC was evaluated in 17 patients with Ga-DOTA-TOC PET/MRI exams, suspected of having neuroendocrine tumors or liver metastases. Effects of CIRCUS sampling for accelerating a data acquisition were evaluated by simulating the data acquisition time retrospectively in increments of 5 s. Effects of MRAC on PET were evaluated using uptake differences in the liver lesions (n = 35), compared to PET with MRAC and MRAC. A Wilcoxon signed-rank test was performed to compare lesion uptakes between the MRAC methods. MRAC showed higher image quality compared to MRAC for the same acquisition times, demonstrating that a data acquisition time of 30 s was reasonable to achieve phase-matched µ-maps. Lesion update differences between MRAC (30 s) versus MRAC (reference, 100 s) were 0.1% ± 1.4% (range of -2.7% to 3.2%) and not significant (P > .05); while, the differences between MRAC versus MRAC were 0.6% ± 11.4% with a large variation (range of -37% to 20%) and significant (P < .05). In conclusion, we demonstrated that a data acquisition of 30 s achieved phase-matched µ-maps when using specialized CIRCUS data sampling and phase-matched µ-maps improved PET quantification significantly.