Positron Emission Tomography (PET) images are prone to motion artefacts due to the long acquisition time of PET measurements. Recently, simultaneous magnetic resonance imaging (MRI) and PET have become available in the first generation of Hybrid MR-PET scanners. In this work, the elimination of artefacts due to head motion in PET neuroimages is achieved by a new approach utilising MR-based motion tracking in combination with PET list mode data motion correction for simultaneous MR-PET acquisitions. The method comprises accurate MR-based motion measurements, an intra-frame motion minimising and reconstruction time reducing temporal framing algorithm, and a list mode based PET reconstruction which utilises the Ordinary Poisson Algorithm and avoids axial and transaxial compression. Compared to images uncorrected for motion, an increased image quality is shown in phantom as well as in vivo images. In vivo motion corrected images show an evident increase of contrast at the basal ganglia and a good visibility of uptake in tiny structures such as superior colliculi.