In this study, we introduce a new design methodology of a granular-oriented self-organizing polynomial neural networks (GoSOPNNs) that is based on multi-layer perceptron with Context-based Polynomial Neurons (CPNs) or Polynomial Neurons (PNs). In contrast to the typical architectures encountered in polynomial neural networks (PNN), our main objective is to develop a methodological design strategy of GoSOPNNs as follows : (a) The 1st layer of the proposed network consists of Context-based Polynomial Neuron (CPN). In here, CPN is fully reflective of the structure encountered in numeric data which are granulated with the aid of Context-based Fuzzy C-Means (C-FCM) clustering method. The context-based clustering supporting the design of information granules is completed in the space of the input data while the build of the clusters is guided by a collection of some predefined fuzzy sets (so-called contexts) defined in the output space. (b) The proposed design procedure being applied at each layer of GoSOPNN leads to the selection of preferred nodes of the network (CPNs or PNs) whose local characteristics (such as the number of contexts, the number of clusters, a collection of the specific subset of input variables, and the order of the polynomial) can be easily adjusted. These options contribute to the flexibility as well as simplicity and compactness of the resulting architecture of the network. For the evaluation of performance of the proposed GoSOPNN network, we describe a detailed characteristic of the proposed model using a well-known learning machine data(Automobile Miles Per Gallon Data, Boston Housing Data, Medical Image System Data).