Nowadays, soft grippers, which use compliant mechanisms instead of stiff components to achieve grasping action, are being utilized in an increasing range of engineering fields, such as food industry, medical care and biological sample collection, for their material selection, high conformability and gentle contact with target objects compared to traditional stiff grippers. In this study, a three-fingered gripper is designed based on a simple actuation mechanism but with high conformability to the object and produces relatively high actuation force per unit mass. The electrostrictive PVDF-based terpolymer is applied as the self-folding actuation mechanism. Finite element analysis (FEA) models are developed to predict the deformation of the folded shape and grasping force of the gripper with two grasp modes, i.e. enveloping grasp and parallel grasp. The FEA models achieved good agreement with experiments. Design optimization is then formulated and a parametric design is conducted with objectives to maximize free deflection and blocked force of the gripper. The design variables are the thicknesses of the active and passive materials, and the nature of the passive layer. It is found that there exists an optimal terpolymer thickness for a given scotch tape substrate thickness to achieve maximum free deflection, and the blocked force always increases as either thickness of terpolymer or scotch tape increases. As the length of the notch increases, free deflection also increases due to more pronounced folding behavior of the actuator, but the blocked force decreases since the actuator is less stiff. The tradeoff between free deflection and blocked force is critical for the final decision on the optimal design for a particular application.