Patients suffering from simultanagnosia cannot perceive more than one object at a time. The underlying mechanism is incompletely understood. One hypothesis is that simultanagnosia reflects "tunnel vision," a constricted attention window around gaze, which precludes the grouping of individual objects. Although this idea has a long history in neuropsychology, the question whether the patients indeed have an abnormal attention gradient around the gaze has so far not been addressed. Here we tested this hypothesis in two simultanagnosia patients with bilateral parieto-occipital lesions and two control groups, with and without brain damage. We assessed the participants' ability to discriminate letters presented briefly at fixation with and without a peripheral distractor or in the visual periphery, with or without a foveal distractor. A constricted span of attention around gaze would predict an increased susceptibility to foveated versus peripheral distractors. Contrary to this prediction and unlike both control groups, the patients' ability to discriminate the target decreased more in the presence of peripheral compared with foveated distractors. Thus, the attentional spotlight in simultanagnosia does not fall on foveated objects as previously assumed, but rather abnormally highlights the periphery. Furthermore, we found the same center-periphery gradient in the patients' ability to recognize multiple objects. They detected multiple, but not single objects more accurately in the periphery than at fixation. These results suggest that an abnormal allocation of attention around the gaze can disrupt the grouping of individual objects into an integrated visual scene.