Previous studies have shown that functional networks are present at birth and change dynamically throughout infancy and early childhood. However, the status of functional connectivity is still poorly understood in patients with infantile esotropia (IE). The aim of this study is to investigate the developmental trends of functional connectivity in patients with IE during a critical period of growth and development. A total of 17 patients with IE (9 males and 8 females; mean age: 3.36 ± 2.03 years, age range: 0.67–6.36 years) and 20 healthy subjects matched for age and gender were recruited and underwent resting-state functional magnetic resonance imaging. The whole-brain functional network connectivity was analyzed for the IE group and healthy control group. A general linear model was applied to assess the group-age interaction in terms of the functional connectivity. The discrepancy between the two groups in functional connectivity trajectories was also quantified across age and exhibited by the quadratic parabolic model. There were significant group-age interactions between the visual network and the default mode network, the visual network and the sensorimotor network, the limbic network and the default mode network, and within the limbic network in the functional connectivity. A U-shaped tendency across age, with an “inflection point” ranging from 3.1 to 4.0 years of age was exhibited in the difference between functional connectivity trajectories of the IE patients and normal controls. Abnormality in functional network connectivity could present in IE patients at birth, exhibiting aberrant developmental patterns over time. An abnormal functional network could reduce the ability of the cortex in visual information processing, further reactivating the subcortical visual information processing system, which is probably the pathogenesis of IE. Three to four years after birth is the critical time window for children with IE to establish normal network connections in the brain. Early surgery during this period may be helpful for affected children to have an opportunity to approach the normal development trajectory as early as possible.