Abstract Background Being able to model a growth curve using three or four non‐linear functional parameters could help explain the growth phenomenon in a precise way and would allow the comparison of an animal's development rate, optimize management and feeding strategies and guide animal production strategies. Objective The goal of this study was to estimate the genetic parameters of growth traits of Isfahan indigenous chicken in Iran and to determine the best non‐linear model describing the growth curve. Methods The prediction of additive genetic parameters was performed using the REML method by WOMBAT. Direct heritability of the studied traits and genetic correlations between them were obtained. The Logistic, Gompertz, von Bertalanffy, Brody, Negative exponential, Weibull, Janoschek and Bridges models were compared based on the coefficient of determination ( R 2 ), mean square error (MSE) and akaike information criterion. Results The Gompertz model was identified as the best model for describing the growth curve for Isfahan native chicken. The heritability of maturity weights ( A ), initial weight ( B ) and maturity rate ( K ) parameters were 0.223 ± 0.002, 0.016 ± 0.005 and 0.087 ± 0.001, respectively. Conclusion This study shows that Isfahan indigenous chicken has the genetic potential for improving growth and reproduction based on their desirable heritabilities and correlations using appropriate models.