Abstract: Large-eddy simulations have been conducted on the interaction of shock/turbulent boundary layer near a convex corner of inflow with Ma_∞=3 and Re_θ=2070. Two typical convex corners, i.e., the sharp and blunt corners, are considered. The geometrical effects of convex corner on the flow structures, unsteady separating flow, and turbulent statistical characteristics are analyzed systematically. For the sharp corner case, locally concentrated favorable pressure gradients are formed near the corner, where the wall friction coefficient obtains a high level. As a result, the separation point is fixed and thus unable to move cross the sharp corner, while the attachment point takes a front/back motion. However, for the blunt corner case, the separation point is not fixed at the corner because of the dispersed distribution of the favorable pressure gradient. As a consequence, both the separation and attachment points become to move front and back. Furthermore, the small scale vortical structures near the separation point are suppressed due to the presence of favorable pressure gradients near the convex corner, while enhanced greatly near the attachment point by the incident shock interaction.