In environmental modeling, the impact of fixed scatterers on the background environment can be effectively accounted for by using numerical Green's functions (NGF), which significantly reduces the number of unknowns in the problem. A recursive solution to acquire NGF using artificial neural networks (ANN) acceleration is presented for multibody scattering scenarios. The recursive method is employed to decompose the multibody problem, transforming the interaction between scatterers into a generalized incident field via NGF. This allows for the decomposition of the scattering characteristics of the multibody problem in the presence of intense oscillations into the effects of single bodies. This decomposition facilitates the accelerated calculation of neural networks. In addition, the scatterers' center positions as prior information can assist the network in extracting data features effectively, leading to an overall improvement in the learning performance of ANN. The implementation of the recursive method combined with ANN acceleration for solving the NGF of the multibody problem not only enhances the accuracy of the neural network acceleration approach but also significantly reduces the overall runtime when compared to the conventional calculation method. Numerical results demonstrate that the relative error of the proposed method accumulates with the recursions and is less than 8.5% after 11 recursions, and the computation time is reduced to about 6.5% of the method of moment.