Abnormal functional connectivity was reported as one of the underlying characteristics of autism spectrum disorder (ASD). Considering the motor deficits in ASD, we utilized praxis to investigate the neural mechanisms of ASD during motor task. Since the previous functional connectivity studies reported divergent results, we explored the properties of the functional connectivity using graph metrics to address brain organization alterations of ASD. We proposed the use of eLORETA to investigate the cortical connectivity during praxis based on a cohort of 45 high-functioning ASD (HFA) children and 45 typically developing (TD) children. The between-group comparison revealed higher clustering coefficient and lower global efficiency for HFA relative to TD while the between-phase comparison suggested decreasing global efficiency, increasing characteristic path length for TD. Nodal metrics exhibited significant differences between groups in frontal and occipital regions. These regions also showed significant changes of nodal metrics and connection strengths between baseline and praxis execution for TD. However, there were no significant changes in global, nodal metrics and connection strengths between phases for HFA. Our study suggested that cortical connectivity in ASD exhibited lower overall efficiency and a deficit in reorganization, which deepens the understanding of abnormal brain organization in ASD.