The mature brain features high wiring efficiency for information transfer. However, the emerging process of such an efficient topology remains elusive. With resting state functional MRI and a large cohort of normal pediatric subjects (n = 147) imaged during a critical time period of brain development, 3 wk- to 2 yr-old, the temporal and spatial evolution of brain network topology is revealed. The brain possesses the small world topology immediately after birth, followed by a remarkable improvement in whole brain wiring efficiency in 1 yr olds and becomes more stable in 2 yr olds. Regional developments of brain wiring efficiency and the evolution of functional hubs suggest differential development trend for primary and higher order cognitive functions during the first two years of life. Simulations of random errors and targeted attacks reveal an age-dependent improvement of resilience. The lower resilience to targeted attack observed in 3 wk old group is likely due to the fact that there are fewer well-established long-distance functional connections at this age whose elimination might have more profound implications in the overall efficiency of information transfer. Overall, our results offer new insights into the temporal and spatial evolution of brain topology during early brain development.