Here we describe a method for measuring tonotopic maps and estimating bandwidth for voxels in human primary auditory cortex (PAC) using a modification of the population Receptive Field (pRF) model, developed for retinotopic mapping in visual cortex by Dumoulin and Wandell (2008). The pRF method reliably estimates tonotopic maps in the presence of acoustic scanner noise, and has two advantages over phase-encoding techniques. First, the stimulus design is flexible and need not be a frequency progression, thereby reducing biases due to habituation, expectation, and estimation artifacts, as well as reducing the effects of spatio-temporal BOLD nonlinearities. Second, the pRF method can provide estimates of bandwidth as a function of frequency. We find that bandwidth estimates are narrower for voxels within the PAC than in surrounding auditory responsive regions (non-PAC).