Hemispheric asymmetry of a wide range of functions is a hallmark of the human brain. The visual system has traditionally been thought of as symmetrically distributed in the brain, but a growing body of evidence has challenged this view. Some highly specific visual tasks have been shown to depend on hemispheric specialization. However, the possible lateralization of cerebral responses to a simple checkerboard visual stimulation has not been a focus of previous studies. To investigate this, we performed two sessions of blood-oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI) in 54 healthy subjects during stimulation with a black and white checkerboard visual stimulus. While carefully excluding possible non-physiological causes of left-to-right bias, we compared the activation of the left and the right cerebral hemispheres and related this to grey matter volume, handedness, age, gender, ocular dominance, interocular difference in visual acuity, as well as line-bisection performance. We found a general lateralization of cerebral activation towards the right hemisphere of early visual cortical areas and areas of higher-level visual processing, involved in visuospatial attention, especially in top-down (i.e., goal-oriented) attentional processing. This right hemisphere lateralization was partly, but not completely, explained by an increased grey matter volume in the right hemisphere of the early visual areas. Difference in activation of the superior parietal lobule was correlated with subject age, suggesting a shift towards the left hemisphere with increasing age. Our findings suggest a right-hemispheric dominance of these areas, which could lend support to the generally observed leftward visual attentional bias and to the left hemifield advantage for some visual perception tasks.