The infant brain experiences explosive growth in the first few years of life. The developing topology of the functional network mirrors the emergence of complex cognitive functions. However, early development of brain topological properties in infants is still largely unclear due to the dearth of high-quality longitudinal infant functional MRI (fMRI) data. In this study, we employed advanced methods to investigate the developmental trajectories of various network features on high-resolution, longitudinal fMRI data of infants from birth to 2 years of age. The developmental trajectories of various global and nodal metrics were evaluated with linear mixed-effect modeling. We then investigated the association between these developmental trajectories and the visual reception ability, an important skill that could shape the future development of other cognitive functions. Four global metrics (shortest path length, global efficiency, local efficiency, and sigma (i.e., small-worldness)) showed significant developmental changes to facilitate more efficient information processing. Significant developmental changes were also found in the nodal characters with a prominent spatial specificity, and some brain regions showed increasing importance along the development. Most importantly, different associations between developmental trajectories in both global and nodal network characters and varied visual reception ability were revealed. This is the first longitudinal study on the early development of the brain functional connectome and its potential relationship to the individual variability of the visual abilities. These findings provide valuable knowledge for better understanding of normative and abnormal neurodevelopment in the first few years of life.