The paper concerns Fuzzy C-Means clustering based fuzzy neural networks (FCM-FNN) and the optimization of the network is carried out by means of hierarchal fair competition-based parallel genetic algorithm (HFCPGA). FCM-FNN is the extended architecture of Radial Basis Function Neural Network (RBFNN). FCM algorithm is used to determine centers and widths of RBFs. In the proposed network, the membership functions of the premise part of fuzzy rules do not assume any explicit functional forms such as Gaussian, ellipsoidal, triangular, etc., so its resulting fitness values directly rely on the computation of the relevant distance between data points by means of FCM. Also, as the consequent part of fuzzy rules extracted by the FCM-FNN model, the order of four types of polynomials can be considered such as constant, linear, quadratic and modified quadratic. Since the performance of FCM-FNN is affected by some parameters of FCM-FNN such as a specific subset of input variables, fuzzification coefficient of FCM, the number of rules and the order of polynomials of consequent part of fuzzy rule, we need the structural as well as parametric optimization of the network. In this study, the HFCPGA which is a kind of multipopulation-based parallel genetic algorithms(PGA) is exploited to carry out the structural optimization of FCM-FNN. Moreover the HFCPGA is taken into consideration to avoid a premature convergence related to the optimization problems. The proposed model is demonstrated with the use of two representative numerical examples.