In the paper, an artificial neural network (ANN) model is proposed to predict the compressive strength of concrete. For developing the ANN model the data bank on concrete compressive strength has been taken from the experiments conducted in the laboratory under standard conditions. The data set is of two types; in one dataset 15% cement is replaced with fly ash and the other one is without any replacement. Several training algorithms, like Quasi-Newton algorithm with Broyden, Fletcher, Goldfarb, and Shanno (BFGS) update (BFG), Fletcher-reeves conjugate gradient algorithm (CGF), Polak-Ribiere conjugate gradient algorithm (CGP),Powell-Beale conjugate gradient algorithm (CGB), Levenberg-Marquardt (LM), Resilient backpropagation (RP), Scaled conjugate gradient backpropagation (SCG), One step Secant backpropagation (OSS) along with various network architectural parameters are experimentally investigated to arrive at the most suitable model for predicting the compressive strength of concrete. It is found that Levenberg-Marquardt (LM) with tan-sigmoid activation function is best for the prediction of compressive strength of concrete. In-situ concrete compressive strength data, based on varying mix proportions, have been taken from one of the research paper present in literature for the validation of the model. It is also recommended that ANN model with the training function, Levenberg-Marquardt (LM) for the prediction of compressive strength of concrete is one of the best possible tool for the purpose.