A model based on a set of differential equations can effectively capture various dynamics. This type of model is therefore ideal for describing genetic networks. Several genetic network inference algorithms based on models of this type have been proposed. Most of these inference methods use models based on a set of differential equations of the fixed form to describe genetic networks. In this study, we propose a new method for the inference of genetic networks. To describe genetic networks, the proposed method does not use models of the fixed form, but uses neural network models. In order to interpret obtained neural network models, we also propose a method based on sensitivity analysis. The effectiveness of the proposed methods is verified through a series of artificial genetic network inference problems.