We discuss a new design methodology of the self-organizing approximator technique (self-organizing polynomial neural networks (SOPNN)) using the evolutionary algorithm (EA). The SOPNN is based on the ideas of group method of data handling. The performances of SOPNN depend strongly on the number of input variables available to the model, and the number of input variables and polynomial type (order) to each node. These variables and polynomial types must be fixed by the designer in advance before the architecture is constructed, and thus, the trial and error method is burdened with heavy computation and low efficiency. Moreover, even after such procedures, the SOPNN may not be the best one. In this paper, we propose an EA-based SOPNN to alleviate these problems. The order of the polynomial, the number of input variables, and the optimum input variables are encoded as a chromosome and the fitness of each chromosome are computed. The appropriate information of each node is evolved accordingly and tuned gradually throughout the EA iterations. We can show that the EA-based SOPNN is a sophisticated and versatile architecture, which can construct models from a limited set of data as well as for poorly defined complex problems. Comprehensive comparisons showed that with a very simple structure, the EA-based SOPNN gave significantly improved performance than the conventional SOPNN model as well as previous identification methods with respect to approximation and prediction abilities.