In aspects of adaptive grip suppression, a wireless device has a display screen with curved display edges to display a selectable element in a region of a curved display edge. The wireless device implements an adaptive control module to adaptively tune grip suppression in the curved display edges of the display screen, which limits a device application action from being initiated based on inadvertent touch inputs on the selectable element. The adaptive control module can adaptively tune the grip suppression by decreasing the grip suppression in the region of the curved display edge proximate the selectable element responsive to false rejects indicating that the device application action is not initiating responsive to intended touch inputs, or by increasing the grip suppression in the region of the curved display edge proximate the selectable element responsive to false accepts indicating that the device application action is initiating responsive to inadvertent touch inputs.