This paper creates a LM (LevenbergMarquardt) algorithm model which is appropriate to solve the problem about weights value of feedforward neural network. On the base of this model, we provide two applications in the oilfield production. Firstly, we simulated the functional relationships between the petrophysical and electrical properties of the rock by neural networks model, and studied oil saturation. Under the precision of data is confirmed, this method can reduce the number of experiments. Secondly, we simulated the relationships between investment and income by the neural networks model, and studied invest saturation point and income growth rate. It is very significant to guide the investment decision. The research result shows that the model is suitable for the modeling and identification of nonlinear systems due to the great fit characteristic of neural network and very fast convergence speed of LM algorithm.