Studying cortical hemispheric asymmetries during the dynamic early postnatal stages in macaque monkeys (with close phylogenetic relationship to humans) would increase our limited understanding on the possible origins, developmental trajectories, and evolutional mechanisms of brain asymmetries in nonhuman primates, but remains a blind spot to the community. Via cortical surface-based morphometry, we comprehensively analyze hemispheric structural asymmetries in 134 longitudinal MRI scans from birth to 20 months of age from 32 healthy macaque monkeys. We reveal that most clusters of hemispheric asymmetries of cortical properties, such as surface area, cortical thickness, sulcal depth, and vertex positions, expand in the first 4 months of life, and evolve only moderately thereafter. Prominent hemispheric asymmetries are found at the inferior frontal gyrus, precentral gyrus, posterior temporal cortex, superior temporal gyrus (STG), superior temporal sulcus (STS), and cingulate cortex. Specifically, the left planum temporale and left STG consistently have larger area and thicker cortices than those on the right hemisphere, while the right STS, right cingulate cortex, and right anterior insula are consistently deeper than the left ones, partially consistent with the findings in human infants and adults. Our results thus provide a valuable reference in studying early brain development and evolution.