This paper uses the recently proposed grasshopper optimization algorithm (GOA) to develop a new hybrid, stochastic training algorithm for the feed-forward neural networks (FFNN). The state-of-the-art hybrid model is then applied to study observing pattern of scour depth which is a challenging problem in hydraulic engineering. In order to verify and control the accuracy, stability, and efficiency of the proposed model and its computational process, the model results are compared to networks trained by three different training algorithms. To achieve this, backpropagation, backpropagation with momentum, and Levenberg-Marquardt learning algorithms, which are widely used for various hydraulic problems, are chosen. The results of the model indicated that the proposed model has high stability and performance in solving regression problems. The comparison of prediction accuracy and convergence curves represented that the model could predict the maximum scour depth with the higher convergence speed. Applying the proposed model improves the correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE) values by approximately 6%, 30%, and 18%, respectively.