Soft manipulators have a broad application prospect in medical, aerospace and other fields due to its excellent environmental adaptability and safe human-machine interaction. However, since the soft manipulator is a kind of continuum robot, the traditional rigid manipulator modeling and control methods cannot be used. For a class of line-driven soft manipulators, modeling methods based on strain parameterization is proposed, which is capable of describing the motion of soft manipulators in three-dimensional space under different wiring methods. First of all, the whole soft manipulator is treated as a Cosserat beam and modeled by the mature Cosserat beam theory, the core idea of which is to discretize the strain field of the soft manipulator by Ritz method to obtain a set of ordinary differential equations, and then the back propagation (BP) neural network is used to complete the drive force conversion between the shape space and the driver space. The 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 the introduction of the adaptive neural network controller is then demonstrated based on Lyapunov's stability theory. Finally, a series of simulation experiments are carried out 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 kind of soft manipulator can be realized.