The study of resting-state functional brain networks is a powerful tool to understand the neurological bases of a variety of disorders such as Autism Spectrum Disorder (ASD). In this work, we have studied the differences in functional brain connectivity between a group of 74 ASD subjects and a group of 82 typical-development (TD) subjects using functional magnetic resonance imaging (fMRI). We have used a network approach whereby the brain is divided into discrete regions or nodes that interact with each other through connections or edges. Functional brain networks were estimated using the Pearson’s correlation coefficient and compared by means of the Network-Based Statistic (NBS) method. The obtained results reveal a combination of both overconnectivity and underconnectivity, with the presence of networks in which the connectivity levels differ significantly between ASD and TD groups. The alterations mainly affect the temporal and frontal lobe, as well as the limbic system, especially those regions related with social interaction and emotion management functions. These results are concordant with the clinical profile of the disorder and can contribute to the elucidation of its neurological basis, encouraging the development of new clinical approaches.