Respiratory motion during cardiac PET acquisitions can cause image blurring and erroneous uptake quantification. In particular the misalignment of attenuation correction (AC) maps and PET emission data can lead to severe quantification errors, because the AC value of the heart is five times higher than of the surrounding lung tissue. Standard PET-MR approaches assume accurate alignment between breathhold MR-based AC maps and free-breathing PET emission data but cannot necessarily ensure it. Here we propose a 75 s free-breathing MR-acquisition, which provides respiratory-resolved AC maps (ACDyn) and non-rigid respiratory motion information. This approach ensures accurate AC for free-breathing PET data and the motion information can be utilized to reduce image blurring caused by respiratory motion. 3D multi-echo MR data was acquired during a 75 s free-breathing scan in six patients. Both a respiratory-resolved dynamic AC map (ACDyn) and a non-rigid respiratory motion field are provided by the MR scan. ACDyn yielded AC values for different breathing phases ensuring accurate AC for each respiratory phase of the free-breathing PET data. In addition, motion-corrected image reconstruction (MCIR) of MR and PET data was used to minimize breathing artefacts. Motion amplitudes in the left ventricle were 8.2 ± 2.9 mm with a dominant motion direction along the anterior-anterolateral and inferior-inferoseptal axis of the heart. The proposed ACDyn-MCIR technique led to significant signal recovery of PET tracer uptake by 24 ± 5% (p < 0.05). The maximum improvement was observed in patients with large misalignment between standard breathhold MR-based AC maps and PET emission data. PET image resolution was improved by 20 ± 12% (p < 0.05). We have presented an efficient MR-scan, which ensures accurate motion information and AC values to improve PET quantification for cardiac PET-MR scans. The short scan time of 75 s makes this free-breathing acquisition easy to integrate into standard clinical PET-MR protocols.