Infancy is a dynamic and immensely important period in human brain development. Studies of infant functional development using resting-state fMRI rely on precisely defined cortical parcellation maps. However, available adult-based functional parcellation maps are not applicable for infants due to their substantial differences in functional organizations. Fine-grained infant-dedicated cortical parcellation maps are highly desired but remain scarce, due to difficulties ranging from acquiring to processing of infant brain MRIs. In this study, leveraging 1,064 high-resolution longitudinal rs-fMRIs from 197 infants from birth to 24 months and advanced infant-dedicated processing tools, we create the first set of infant-specific, fine-grained cortical functional parcellation maps. Besides the conventional folding-based cortical registration, we specifically establish the functional correspondences across individuals using functional gradient densities and generate both age-specific and age-common fine-grained parcellation maps. The first set of comprehensive brain functional developmental maps are accordingly derived, and reveals a complex, hitherto unseen multi-peak fluctuation development pattern in temporal variations of gradient density, network sizes, and local efficiency, with more dynamic changes during the first 9 months than other ages. Our proposed method is applicable in generating fine-grained parcellations for the whole lifespan, and our parcellation maps will be available online to advance the neuroimaging field.