Summary: We introduce a new topology of Fuzzy Polynomial Neural Networks (FPNN) that is based on a genetically optimized multilayer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology. The underlying methodology involves mechanisms of genetic optimization, especially genetic algorithms (GAs). Let us recall that the design of the “conventional” FPNNs uses an extended Group Method of Data Handling (GMDH) and exploits a fixed fuzzy inference type located at each FPN of the FPNN as well as considers a fixed number of input nodes at FPNs (or nodes) located in each layer. The proposed FPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional FPNNs. The structural optimization is realized via GAs whereas in the case of the parametric optimization we proceed with a standard least square method based learning. Through the consecutive process of such structural and parametric optimization, an optimized and flexible fuzzy neural network is generated in a dynamic fashion. The performance of the proposed gFPNN is quantified through experimentation that exploits standard data already being used in fuzzy modeling. The results reveal superiority of the proposed networks over the existing fuzzy and neural models.