The brain combines visual information from the two eyes and forms a coherent percept, even when inputs to the eyes are different. However, it is not clear how inputs from the two eyes are combined in visual cortex. We measured fMRI responses to single gratings presented monocularly, or pairs of gratings presented monocularly or dichoptically with several combinations of contrasts. Gratings had either the same orientation or orthogonal orientations (i.e., plaids). Observers performed a demanding task at fixation to minimize top-down modulation of the stimulus-evoked responses. Dichoptic presentation of compatible gratings (same orientation) evoked greater activity than monocular presentation of a single grating only when contrast was low (<10%). A model that assumes linear summation of activity from each eye failed to explain binocular responses at 10% contrast or higher. However, a model with binocular contrast normalization, such that activity from each eye reduced the gain for the other eye, fitted the results very well. Dichoptic presentation of orthogonal gratings evoked greater activity than monocular presentation of a single grating for all contrasts. However, activity evoked by dichoptic plaids was equal to that evoked by monocular plaids. Introducing an onset asynchrony (stimulating one eye 500 ms before the other, which under attentive vision results in flash suppression) had no impact on the results; the responses to dichoptic and monocular plaids were again equal. We conclude that when attention is diverted, inter-ocular suppression in V1 can be explained by a normalization model in which the mutual suppression between orthogonal orientations does not depend on the eye of origin, nor on the onset times, and cross-orientation suppression is weaker than inter-ocular (same orientation) suppression.