We present a high-dimensional model of the representational space in human ventral temporal (VT) cortex in which dimensions are response-tuning functions that are common across individuals and patterns of response are modeled as weighted sums of basis patterns associated with these response tunings. We map response-pattern vectors, measured with fMRI, from individual subjects' voxel spaces into this common model space using a new method, "hyperalignment." Hyperalignment parameters based on responses during one experiment--movie viewing--identified 35 common response-tuning functions that captured fine-grained distinctions among a wide range of stimuli in the movie and in two category perception experiments. Between-subject classification (BSC, multivariate pattern classification based on other subjects' data) of response-pattern vectors in common model space greatly exceeded BSC of anatomically aligned responses and matched within-subject classification. Results indicate that population codes for complex visual stimuli in VT cortex are based on response-tuning functions that are common across individuals.