A novel framework for inverse quantitative structure–activity relationships (inverse QSAR) has recently been proposed and developed using both artificial neural networks and mixed integer linear programming. However, classes of chemical graphs treated by the framework are limited. In order to deal with an arbitrary graph in the framework, we introduce a new model, called a two-layered model, and develop a corresponding method. In this model, each chemical graph is regarded as two parts: the exterior and the interior. The exterior consists of maximal acyclic induced subgraphs with bounded height, the interior is the connected subgraph obtained by ignoring the exterior, and the feature vector consists of the frequency of adjacent atom pairs in the interior and the frequency of chemical acyclic graphs in the exterior. Our method is more flexible than the existing method in the sense that any type of graphs can be inferred. We compared the proposed method with an existing method using several data sets obtained from PubChem database. The new method could infer more general chemical graphs with up to 50 non-hydrogen atoms. The proposed inverse QSAR method can be applied to the inference of more general chemical graphs than before.