Neuronal oscillations at about 10 Hz, called alpha oscillations, are often thought to arise from synchronous activity across large regions of occipital cortex, reflecting general cognitive states such as arousal and alertness. However, there is also evidence that modulation of alpha oscillations in the visual cortex can be spatially specific. Here, we used intracranial electrodes in human patients to measure alpha oscillations in multiple visual areas in response to visual stimuli whose location varied systematically across the visual field. We used a model-based approach to separate the alpha oscillatory power from broadband power changes. The variation in alpha oscillatory power with stimulus position was then fitted by a population receptive field (pRF) model. We find that the alpha pRFs have similar center locations to pRFs estimated from broadband (70–180 Hz) time series, but are several times larger. The results demonstrate that alpha suppression in the human visual cortex can be precisely tuned. In addition, the large, negative alpha pRF indicates that visual stimulation suppresses alpha oscillations and likely increases cortical excitability over a large cortical extent, predicting many of the effects observed in exogenous visual attention experiments. These findings provide further links between the alpha oscillation and spatial attention.