How brain functional architecture differs across people is a key question of human neuroscience, and understanding these differences is critical for building brain-based biomarkers. However, current individualized models of brain functional organization are based on brain regions and networks, limiting their use to study fine-grained vertex- or voxel-level differences. In this work, we present the Individualized Neural Tuning (INT) model, a fine-grained individualized model of brain functional organization. The first part of the INT model models each individual’s brain responses as a linearly transformed functional template, such that it captures both functional and topographic idiosyncrasies. The second part of the INT model factorizes the modeled brain responses, separating temporal information capturing how the stimulus changes over time (shared across individuals) and stimulus-general neural tuning (specific to each individual and each cortex). The two parts of the INT model are designed in such a way that (a) the INT model has vertex-level granularity; (b) it models both functional differences and topographic differences; and (c) the modeled neural tuning is stimulus-general in that it generalizes to new stimuli. Through a series of analyzes, we demonstrate that (a) the modeled brain functional organization is highly specific to the individual and reliable across independent data; (b) the model can predict an individual’s responses to new stimuli based on others’ responses, including category selectivity maps and retinotopic maps; (c) the model can predict fine-grained response patterns, which can be used to distinguish responses to different time points of a movie; (d) the model performance keeps improving with more data, but 10–20 minutes of movie are usually sufficient for good performance. Together, these analyses demonstrate that the INT model affords an individualized fine-grained model of brain functional architecture, which is reliable, precise, and generalizable across stimuli.