In this research, a cell-by-cell artificial neural network approach is used to predict the velocity vectors of steady-state, viscous, incompressible, laminar flows in a two-dimensional computational domain. The flow behaviour is characterized by the initial flow velocity, and the geometry of the wall boundaries. A feedforward neural network architecture is applied in this research. The model is trained using Levenberg-Marquardt and Bayesian regularization backpropagation algorithms. The training data for the model are obtained by solving the Navier-Stokes equations for two-dimensional, steady-state, viscous, incompressible, laminar flow using commercial ANSYS Fluent software. The results show that the predicted values produced by the model is in good agreement with the simulation data. Even though the introduction of artificial neural networks at the cell level increases the complexity of the training process, this drawback is compensated by the increase in flexibility (generality) of the model. More importantly, the results show that the cell-by-cell artificial neural network approach is capable of providing an accurate prediction of the fluid velocity field for the flow investigated in this research. The outcomes designate that the new ANN approach is capable of getting an accurate velocity vector prediction as several statistical parameters confirmed. Since all the computation cost took place in the training phase, the new approach calculated the result faster than the traditional numerical methods. Such simulation provides a reliable perception about the fluid behaviour with respect to momentum and equations. In addition to the preceding recorded data, the proposed method considers the geometrical boundaries profile as a major contribution for ANN training phase. ©2006-2016 Asian Research Publishing Network (ARPN).