A breeder hybrid algorithm consisting of the constitution of nonlinear regression-based breeder genetic algorithm and simulated annealing is proposed for the objective of forecasting the natural gas demand with a smaller error rate. The main aim of this study is to show general natural gas demand forecasting model of the breeder hybrid algorithm based nonlinear regression. The most important difference that distinguishes this natural gas demand forecasting model from other models in the literature is that the proposed model evolves continuously with the best solutions in both the breeder genetic algorithm and simulated annealing parts. It is applied to Turkey natural gas demand forecasting to show its superiority and applicability. The consumption amount of natural gas has between 1985 and 2000 is determined as dependent variable whereas the independent variables are determined as the gross national product, population and the growth rate. Then, the consumption amounts of natural gas between 2001 and 2014 are forecasted with significantly small MAPE values that are obtained 0.0188 and 0.0143 for year 2014 using the proposed algorithms and compared to different solutions in the literature. The proposed algorithms are superior to the comparable algorithms in the literature. Then, two scenarios are applied for the years between 2015 and 2030 for future projection. (C) 2017 Elsevier Ltd. All rights reserved.