In this study, an artificial neural network (ANN) model for studying the strength properties of steel fiber reinforced concrete (SFRC) containing fly ash was devised. The mixtures were prepared with 0 wt%, 15 wt%, and 30 wt% of fly ash, at 0 vol.%, 0.5 vol.%, 1.0 vol.% and 1.5 vol.% of fiber, respectively. After being cured under the standard conditions for 7, 28, 90 and 365 d, the specimens of each mixture were tested to determine the corresponding compressive and flexural strengths. The parameters such as the amounts of cement, fly ash replacement, sand, gravel, steel fiber, and the age of samples were selected as input variables, while the compressive and flexural strengths of the concrete were chosen as the output variables. The back propagation learning algorithm with three different variants, namely the Levenberg-Marquardt (LM), scaled conjugate gradient (SCG) and Fletcher-Powell conjugate gradient (CGF) algorithms were used in the network so that the best approach can be found. The results obtained from the model and the experiments were compared, and it was found that the suitable algorithm is the LM algorithm. Furthermore, the analysis of variance (ANOVA) method was used to determine how importantly the experimental parameters affect the strength of these mixtures.