In the last decade, different positron emission tomography (PET) crystals have been proposed for brain PET detectors. Brain PET cameras with restricted field of view to a smaller size to cover the brain can both exhibit significantly higher performance and lower the cost when compared to conventional whole-body PET scanners. The existing designs based on scintillation crystals employ the most commonly known materials such as lutetium oxyorthosilicate and bismuth germanate. This is due to their relatively good parameters such as high light yield and density. The main drawback of using scintillation crystals is that they have a modest energy resolution. In this study, a brain PET scanner was designed and simulated using a Geant4 Application for Tomographic Emission (GATE) toolkit. The performances of five crystals, namely strontium hafnate, gadolinium aluminium gallium garnet, gadolinium yttrium gallium aluminium garnet, gadolinium lutetium gallium aluminium garnet, and lutetium oxyorthosilicate for comparison, were evaluated in terms of sensitivity, spatial resolution, and count rate. The performance evaluation results showed that among the suggested scintillators, strontium hafnate can be considered as a promising alternative detector for high performance brain PET systems.