The human brain has long inspired the pursuit of artificial intelligence (AI). Recently, neuroimaging studies provide compelling evidence of alignment between the computational representation of artificial neural networks (ANNs) and the neural responses of the human brain to stimuli, suggesting that ANNs may employ brain-like information processing strategies. While such alignment has been observed across sensory modalities--visual, auditory, and linguistic--much of the focus has been on the behaviors of artificial neurons (ANs) at the population level, leaving the functional organization of individual ANs that facilitates such brain-like processes largely unexplored. In this study, we bridge this gap by directly coupling sub-groups of artificial neurons with functional brain networks (FBNs), the foundational organizational structure of the human brain. Specifically, we extract representative patterns from temporal responses of ANs in large language models (LLMs), and use them as fixed regressors to construct voxel-wise encoding models to predict brain activity recorded by functional magnetic resonance imaging (fMRI). This framework links the AN sub-groups to FBNs, enabling the delineation of brain-like functional organization within LLMs. Our findings reveal that LLMs (BERT and Llama 1-3) exhibit brain-like functional architecture, with sub-groups of artificial neurons mirroring the organizational patterns of well-established FBNs. Notably, the brain-like functional organization of LLMs evolves with the increased sophistication and capability, achieving an improved balance between the diversity of computational behaviors and the consistency of functional specializations. This research represents the first exploration of brain-like functional organization within LLMs, offering novel insights to inform the development of artificial general intelligence (AGI) with human brain principles.