This paper introduces a shape memory alloy-based gripper for grasping flat objects with gecko-inspired adhesives. Compared to other grippers that utilize gecko-inspired adhesives, the gripper presented here is less expensive, lighter, simpler, and smaller, while still maintaining the ability to control the adhesive pressure. To verify the applicability of proposed gripper, experiments were conducted on a variety of substrates. Experimental results demonstrated 3.3, 2.75, 2.3, and 2.2 kPa average normal adhesion pressure on the surface of carbon fiber, acrylic, glass, and steel, respectively. These adhesion levels are on par with other grippers that use microstructured, gecko-like adhesives.