The contrast detection threshold of a grating located in the periphery is increased if a surrounding grating of the same frequency and orientation is present. This inhibition between center and surround has been termed surround suppression. In this work we measured the spatial frequency bandwidth of surround suppression in the periphery for different spatial frequencies (0.5, 1.1, 3, and 5 cycles/deg) of a sinusoidal grating (target) surrounded by a grating with different spatial frequencies (surround). Using a Bayesian adaptive staircase, we measured contrast detection thresholds in an 8AFC detection task in which the target (grating with a 2.3-deg Butterworth window) could appear in one of eight possible positions at 4° eccentricity. The target was surrounded by a grating (with a 18° Butterworth window) with the same or an orthogonal orientation. In each session we fixed the spatial frequency of the target and changed the spatial frequency and the orientation of the surround. When the surround was orthogonal to the target, the thresholds were similar to those obtained without surround, independent of the surrounding spatial frequency. However, when the target and surround had the same orientation and spatial frequency, the contrast threshold was increased by a factor ranging from 3 to 6 across subjects. This suppression reduced rapidly as the spatial frequency of the surround moved away from that of the target. The bandwidth of the suppressive effect depended on spatial frequency, declining from 2.9 octaves at 0.5 c/deg to 1 octave for frequencies above 3 c/deg. This is consistent with the bandwidth of individual simple cells in visual cortex and of spatial frequency channels measured psychophysically, both of which decline with increasing spatial frequency. This suggests that surround suppression may be due to relatively precise inhibition by cells with the same tuning as the target.