Pneumatic soft actuators are fundamental and critical components of pneumatic soft robot, offering unparalleled advantages in achieving bending motions. However, the nonlinearity of both structure and material property presents great challenge for modeling and control of soft actuators. Based on the assumption of piecewise constant curvature deformation, Yeoh hyperelastic material constitutive model, and the virtual work principle, a bending model of a pneumatic networks ( pneu-net) soft actuator with constant curvature is established in this paper. Finite element simulations were conducted to investigate the effects of structural parameters and input air pressure on the bending performance of the actuator. On this basis, a variable parameter variable curvature actuator design was proposed, and a predictive model for its bending deformation was established. Consistency error analysis for multiple actuators was performed, and the model′ s validity was verified through finite element simulations and experiments. Finally, the force output characteristics of the soft actuators were experimentally tested. A three-finger soft gripper was developed, and the performance of gripping different objects was shown by experiments.