Surface curvature has been shown to have significant effects on the film cooling performance of round holes, but the literature includes few studies of its effects on shaped holes despite their prevalence in gas turbines. Experiments were performed using two rows of holes placed on the suction side of a scaled-up turbine blade in a low-Mach-number linear cascade wind tunnel with low freestream turbulence. The rows were placed in regions of high and low convex surface curvature, respectively. Geometries and flow conditions for the rows were matched to those from previous flat plate studies. Comparison of the adiabatic effectiveness results from the high curvature and flat plate rows revealed the same trends as those in the literature using round holes — with increased performance for the high curvature row at lower blowing ratios and the opposite at higher ones. The low curvature row had similar performance to the flat plate row at lower blowing ratios, suggesting the mild convex curvature had little beneficial effect. At higher blowing ratios, the low curvature row had inferior performance, which was attributed to the local freestream adverse pressure gradient that generated additional turbulence, promoting jet-to-mainstream mixing and decreasing performance.