In small animal positron emission tomography (PET) studies, given the spatial resolution of preclinical PET scanners, quantification in small regions can be challenging. Moreover, in scans where animals are placed away from the center of the field of view (CFOV), e.g. in simultaneous scans of multiple animals, quantification accuracy can be compromised due to the loss of spatial resolution towards the edge of the FOV. Here, we implemented a spatially variant resolution model to improve quantification in small regions and to allow simultaneous scanning of multiple animals without compromising quantification accuracy. The scanner's point spread function (PSF) was characterized across the FOV and modelled using a spatially variant and asymmetric Gaussian function. The spatially variant PSF (SVPSF) was then used for resolution modelling in the iterative reconstruction. To assess the image quality, a line source phantom in a cold and warm background, as well as mouse brain [18F]FDG scans, were performed. The SVPSF and the vendor's maximum a posteriori (MAP3D) reconstructions produced uniform spatial resolution across the scanner FOV, but MAP3D resulted in lower spatial resolution. The line sources recovery coefficient using SVPSF was similar at the CFOV and at the edge of the FOV. In contrast, the other tested reconstructions produced lower recovery coefficient at the edge of the FOV. In mouse brain reconstructions, less spill-over from hot regions to cold regions, as well as more symmetric regional brain uptake was observed using SVPSF. The contrast in brain images was the highest using SVPSF, in mice scanned at the CFOV and off-center. Incorporation of a spatially variant resolution model for small animal brain PET improves quantification accuracy in small regions and produces consistent image spatial resolution across the FOV. Therefore, simultaneous scanning of multiple animals can benefit by using spatially variant resolution modelling.