The brain presents a real complex network of modular, small-world, and hierarchical nature, which are features of non-Euclidean geometry. Using resting-state functional magnetic resonance imaging, we constructed a scale-free binary graph for each subject, using internodal time series correlation of regions of interest as a proximity measure. The resulting network could be embedded onto manifolds of various curvatures and dimensions. While maintaining the fidelity of embedding (low distortion, high mean average precision), functional brain networks were found to be best represented in the hyperbolic disc. Using the 𝕊 1 /ℍ 2 model, we reduced the dimension of the network into two-dimensional hyperbolic space and were able to efficiently visualize the internodal connections of the brain, preserving proximity as distances and angles on the hyperbolic discs. Each individual disc revealed relevance with its anatomic counterpart and absence of center-spaced node. Using the hyperbolic distance on the 𝕊 1 /ℍ 2 model, we could detect the anomaly of network in autism spectrum disorder subjects. This procedure of embedding grants us a reliable new framework for studying functional brain networks and the possibility of detecting anomalies of the network in the hyperbolic disc on an individual scale. Author Summary Human brain networks possess modular, small-world, and hierarchical natures, which necessitate the inspection of network in a basis of non-Euclidean geometry. In this work, using the time series correlation of BOLD signals from resting-state functional magnetic resonance imaging, we constructed a scale-free network for each individual subject and embedded the networks into hyperbolic discs of the 𝕊 1 /ℍ 2 model. The embedding procedure showed reproducibility, and the embedded discs showed relevance with their anatomical counterparts. Then, we assessed the anomaly of brain networks in subjects with autism spectrum disorder by comparing hyperbolic distances of edges. This procedure leads us to a new method of reproducible visualization of functional brain networks and the possibility of detecting anomalies of internodal pathways in the brain network of a diseased subject, on an individual scale.