The firing rates of neurons in primary visual cortex (V1) are suppressed by large stimuli, an effect known as surround suppression. In cats and monkeys, the strength of suppression is sensitive to orientation; responses to regions containing uniform orientations are more suppressed than those containing orientation contrast. This effect is thought to be important for scene segmentation, but the underlying neural mechanisms are poorly understood. We asked whether it is possible to study these mechanisms in the visual cortex of mice, because of recent advances in technology for studying the cortical circuitry in mice. It is unknown whether neurons in mouse V1 are sensitive to orientation contrast. We measured the orientation selectivity of surround suppression in the different layers of mouse V1. We found strong surround suppression in layer 4 and the superficial layers, part of which was orientation tuned: iso-oriented surrounds caused more suppression than cross-oriented surrounds. Surround suppression was delayed relative to the visual response and orientation-tuned suppression was delayed further, suggesting two separate suppressive mechanisms. Previous studies proposed that surround suppression depends on the activity of inhibitory somatostatin-positive interneurons in the superficial layers. To test the involvement of the superficial layers we topically applied lidocaine. Silencing of the superficial layers did not prevent orientation-tuned suppression in layer 4. These results show that neurons in mouse V1, which lacks orientation columns, show orientation-dependent surround suppression in layer 4 and the superficial layers and that surround suppression in layer 4 does not require contributions from neurons in the superficial layers.