Rainfall-Runoff (RR) modelling is a key component of water resource management. Because the relationship between rainfall and runoff is a complex natural event, it necessitates extensive computation. Runoff response is influenced by several interconnected phenomena, including rainfall intensity, geomorphology, climate, and landscape. The present study examines the rainfall-runoff-based model development by using artificial neural networks (ANNs) models in the Yerli sub-catchment of the upper Tapi basin for a period of 36 years, i.e., from 1981–2016. The created ANN models were capable of establishing the correlation between input and output data sets. The rainfall and runoff models that were built have been calibrated and validated. For predicting runoff, Feed Forward Back Propagation Neural Network (FFBPNN) and Cascade Forward Back Propagation Neural Network (CFBPNN) models are used. The efficacy of the model is evaluated by various measures such as mean square error (MSE), root mean square error (RMSE), and coefficient of correlation (R). With MSE, RMSE, and R values of 0.4982, 0.7056, and 0.96213, respectively, FFBPNN outperforms two networks with model architectures of 6-4-1 and Transig transfer function. Also, in this study, the Levenberg-Marquardt (LM), Bayesian Regularization (BR), and Conjugate Gradient Scaled (CGS) algorithms are used to train the ANN rainfall-runoff models. The results show that LM creates the most accurate model. It performs better than BR and CGS. The best model is the LM trained method with 30 neurons, which has MSE values of 0.7279, RMSE values of 0.8531, and R values of 0.95057. It is concluded that the constructed neural network model was capable of quite accurately predicting runoff for the Yerli sub-catchment.