Divisive normalization of the neural responses by the activity of the neighboring neurons has been proposed as a fundamental operation in the nervous system based on its success in predicting neural responses recorded in primate electrophysiology studies. Nevertheless, experimental evidence for the existence of this operation in the human brain is still scant. Here, using functional MRI, we examined the role of normalization across the visual hierarchy in the human visual cortex. Using stimuli form the two categories of human bodies and houses, we presented objects in isolation or in clutter and asked participants to attend or ignore the stimuli. Focusing on the primary visual area V1, the object-selective regions LO and pFs, the body-selective region EBA, and the scene-selective region PPA, we first modeled single-voxel responses using a weighted sum, a weighted average, and a normalization model and demonstrated that although the weighted sum and weighted average models also made acceptable predictions in some conditions, the response to multiple stimuli could generally be better described by a model that takes normalization into account. We then determined the observed effects of attention on cortical responses and demonstrated that these effects were predicted by the normalization model, but not by the weighted sum or the weighted average models. Our results thus provide evidence that the normalization model can predict responses to objects across shifts of visual attention, suggesting the role of normalization as a fundamental operation in the human brain.