Abstract: With the vigorous development of material synthesis, mechanical manufacturing, and computer technology, as well as the in-depth study of control theory and bionics, robotics has undergone tremendous changes in recent decades. From rigid robots to discrete redundancy robots, from continuum robots to soft robots, the application of robots has long been beyond traditional industrial fields such as assembly, welding, and painting. It has expanded to medicine, education, agriculture, the military, etc., covering almost every aspect of people's lives. Soft manipulators have broad application prospects in medicine, aerospace engineering, and other fields due to their excellent environmental adaptability and safe human–machine interaction. However, soft robots comprise flexible materials and often have no internal support structure, so their ends have a very limited carrying capacity. To compensate for this inadequacy, soft robots usually use the bending of the entire body to grasp objects or operate underwater to partially counteract gravity. In addition, the deformation state of a soft robot is difficult to estimate when it is affected by external force or in contact with the environment, which also causes many difficulties in the modeling and control of soft robots. In the case of inaccurate modeling and poor controllability, the accessibility and accuracy of its end are bound to be greatly compromised. For a class of line-driven soft manipulators, a modeling method based on strain parameterization is proposed that can describe the motion of soft manipulators in three-dimensional space under different wiring methods. First, the entire soft manipulator is treated as a Cosserat beam and modeled by the mature Cosserat beam theory, wherein the strain field of the soft manipulator is discretized using the Ritz method to obtain a set of ordinary differential equations, and then a back propagation (BP) neural network is used to complete the drive force conversion between the shape and driver spaces. A radial basis function (RBF) neural network is used to approximate and compensate for the unknown dynamics present in the soft manipulator model. The stability of the closed-loop system after introducing the adaptive neural network controller is then demonstrated on the basis of Lyapunov's stability theory. Finally, a series of simulation experiments are performed for the model and the adaptive neural network controller to verify the effectiveness of the model and the control algorithm. Therefore, the modeling control of a type of soft manipulator is realized.