Frequency selectivity is a ubiquitous property of auditory neurons. Measuring it in human auditory cortex may be crucial for understanding common auditory deficits, but current non-invasive neuroimaging techniques can only measure the aggregate response of large populations of cells, thereby overestimating tuning width. Here we attempted to estimate neuronal frequency tuning in human auditory cortex using a combination of fMRI-adaptation paradigm at 7T and computational modelling. We measured the BOLD response in the auditory cortex of eleven participants to a high frequency (3.8 kHz) probe presented alone or preceded by adaptors at different frequencies (0.5 to 3.8 kHz). From these data, we derived both the response tuning curves (the BOLD response to adaptors alone as a function of adaptor frequency) and adaptation tuning curves (the degree of response suppression to the probe as a function of adaptor frequency, assumed to reflect neuronal tuning) in primary and secondary auditory cortical areas, delineated in each participant. Results suggested the existence of both frequency-independent and frequency-specific adaptation components, with the latter being more frequency-tuned than response tuning curves. Using a computational model of neuronal adaptation and BOLD non-linearity in topographically-organized cortex, we demonstrate both that the frequency-specific adaptation component overestimates the underlying neuronal frequency tuning and that frequency-specific and frequency-independent adaptation component cannot easily be disentangled from the adaptation tuning curve. By fitting our model directly to the response and adaptation tuning curves, we derive a range of plausible values for neuronal frequency tuning. Our results suggest that fMRI adaptation is suitable for measuring neuronal frequency tuning properties in human auditory cortex, provided population effects and the non-linearity of BOLD response are taken into account.