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For quantitative and visually consistent brain imaging on positron emission tomography magnetic resonance imaging systems, a minimum of three tissue classes are needed for MR-based attenuation correction (MRAC): soft tissue, air, and bone. However, gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF) have a higher attenuation value than soft tissue. In addition, a continuous $\mu $-value for bone is desired as bone density varies across the skull. In this paper, we evaluated the effect of brain tissue and implemented a continuous template-based skull for MRAC, using a previously introduced tissue-probability-based attenuation correction (TPB-AC) method. The method allows deriving an MR-based attenuation map ($\mu $-map) from T1-weighted MR images. The procedures to implement GM, WM, CSF, and continuous skull to TPB-AC method are described. MR-based $\mu $-maps with 3, 4, and 6 tissue classes using discrete segmentation-based and continuous template-based skull were created. The 3-class $\mu $-map included air, soft tissue, and bone. The 4-class $\mu $-map included an additional brain tissue class defined as the mean value of GM, WM, and CSF. The 6-class $\mu $-map included all individual tissue classes. A visual and quantitative comparison of PET images reconstructed with six different MR-based $\mu $-maps was performed by using computed tomography (CT)-based attenuation correction (CTAC) as reference. The MR-based $\mu $-maps were evaluated against CTAC for similarity in structures containing bone, brain, soft tissue, and air. The quantitative accuracy of MRAC-reconstructed PET was evaluated by comparison of ratio images, linear regression plots and regional volume of interest (VOI) analysis against CTAC reconstructed PET data. Results show that accounting the higher attenuation in the brain tissue reduces the underestimation seen in PET images reconstructed with 3-class MRAC. No major difference existed between 4-class and 6-class MRAC to account for higher attenuation of the brain. The quantitative bias in PET between a discrete segmentation-based skull and continuous template-based skull was similar. Segmentation-based skull resulted in better delineation of individual anatomy. The whole-brain error across all VOI was: −3.77% (±1.95%) and −4.14% (±2.07%) with 3-class MRAC with discrete and continuous skull, −0.74% (±1.87%) and −1.70% (±1.96%) with 4-class MRAC, −0.69% (±2.07%) and −1.65% (±1.96%) with 6-class MRAC. Therefore, a 4-class $\mu $-map accounting for soft tissue, air, bone, and brain at minimum with either discrete segmentation-based or continuous template-based skull is applicable for improving the quantitative accuracy of MRAC. Further development is needed to accurately define optimal attenuation coefficients for brain tissues and to improve the registration and delineation of the CT template-based skull.