Investigating cerebral asymmetries in non-human primates would facilitate to understand the evolutional traits of the human brain specialization related to language and other high-level cognition. However, brain asymmetrical studies of monkeys produced controversial results. Here, we investigated the cerebral asymmetries using a combination of the optimized voxel-based morphometry (VBM) and tract-based spatial statistics (TBSS) protocols in monkeys. The study-specific MRI and DTI-based templates were created in 66 adult Macaca fascicularis, and the asymmetrical index of grey and white matter was subsequently examined. The VBM analysis detected the well-known frontal and occipital petalias and confirmed the presence of leftward asymmetry in the ventral frontal cortex. A marked leftward asymmetry of anterior superior temporal gyrus but not posterior portion were found. We also identified grey matter asymmetries in some regions that were not previously reported including rightward anterior cingulate, insular cortex and thalamus, and leftward caudate. In contrast, the results of TBSS analysis for the first time revealed the robust leftwards asymmetries of corpus callosum (splenium and body), internal/external capsule, and white matter in middle temporal gyrus, adjacent thalamus and amygdala whereas the rightwards in uncinate fasciculus, posterior thalamic radiation and cerebral peduncle. These findings provide robust evidence of grey and white matter asymmetries in the brain of monkeys, which may extend the understanding of brain evolution in cerebral specialization.