In this paper, we presented a data-driven framework to optimize the out-of-plane stiffness for soft grippers to achieve mechanical properties as hard-to-twist and easy-to-bend. The effectiveness of this method is demonstrated in the design of a soft pneumatic bending actuator (SPBA). First, a new objective function is defined to quantitatively evaluate the out-of-plane stiffness as well as the bending performance. Then, sensitivity analysis is conducted on the parametric model of an SPBA design to determine the optimized design parameters with the help of Finite Element Analysis (FEA). To enable the computation of numerical optimization, a data-driven approach is employed to learn a cost function that directly represents the out-of-plane stiffness as a differentiable function of the design variables. A gradient-based method is used to maximize the out-of-plane stiffness of the SPBA while ensuring specific bending performance. The effectiveness of our method has been demonstrated in physical experiments taken on 3D-printed grippers.