Socio-communicative impairments are salient features of autism spectrum disorder (ASD) from a young age. The anterior prefrontal cortex (aPFC), or Brodmann area 10, is a key processing area for social function, and atypical development of this area is thought to play a role in the social deficits in ASD. It is important to understand these brain functions in developing children with ASD. However, these brain functions have not yet been well described under conscious conditions in young children with ASD. In the present study, we focused on the brain hemodynamic functional connectivity between the right and the left aPFC in children with ASD and typically developing (TD) children and investigated whether there was a correlation between this connectivity and social ability. Brain hemodynamic fluctuations were measured non-invasively by near-infrared spectroscopy (NIRS) in 3- to 7-year-old children with ASD (n = 15) and gender- and age-matched TD children (n = 15). The functional connectivity between the right and the left aPFC was assessed by measuring the coherence for low-frequency spontaneous fluctuations (0.01-0.10 Hz) during a narrated picture-card show. Coherence analysis demonstrated that children with ASD had a significantly higher inter-hemispheric connectivity with 0.02-Hz fluctuations, whereas a power analysis did not demonstrate significant differences between the two groups in terms of low frequency fluctuations (0.01-0.10 Hz). This aberrant higher connectivity in children with ASD was positively correlated with the severity of social deficit, as scored with the Autism Diagnostic Observation Schedule. This is the first study to demonstrate aberrant brain functional connectivity between the right and the left aPFC under conscious conditions in young children with ASD.