Artificial Neural Networks (ANN) are used in place of expensive models to reduce the computational burden required for reliability analysis. Often, ANNs with selected architecture are trained with the back-propagation algorithm from few data representatives of the input/output relationship of the underlying model of interest. However, different performing ANNs might be obtained from the same training data, leading to an uncertainty in selecting the best performing ANN. On the other hand, using cross-validation to select the best performing ANN based on the highest R2 value can lead to a biassing in terms of the prediction made by the selected ANN. This is due to the fact that the use of R2 cannot determine if the prediction made by ANN is biased. Additionally, R2 does not indicate if a model is adequate, as it is possible to have a low R2 for a good model and a high R2 for a bad model. Hence we propose an approach to improve the prediction robustness of an ANN based on coupling Bayesian framework and model averaging technique into a unified framework. The model uncertainties propagated to the robust prediction is quantified in terms of confidence intervals. Two examples are used to demonstrate the applicability of the approach.