Compared to traditional grippers, soft grippers can typically grasp a wider range of objects, including ones that are soft, fragile, or irregularly shaped, but at the cost of a relatively low gripping force. To increase gripping force for soft grippers, this research presents a gripper with an integrated electrostatic and gecko-inspired adhesive. Synthetic gecko-inspired, microstructured adhesives are controllable (i.e. they can be turned on and off) and work on a wide range of substrates and materials; however, they are not typically effective on rough surfaces. In contrast, electrostatic adhesives, also controllable, have a higher tolerance to rough surfaces. By combining the two, it is possible to create an adhesive that is effective on a wider range of materials and roughness, including fabric. To increase the gripping force, parameters that affect electrostatic adhesion, including the electrode gap, electrode width, relative permittivity of gecko-inspired layer, and air gap between the adhesive and substrate were studied with Comsol Multiphysics software and experimentally validated. Results show that adding the two adhesives improves the gripping capabilities across acrylic, Tyvek fabric, and Kapton hemispheres of different diameters on an average of 100, 39, and 168%, respectively.