The occurrence frequency of drought has intensified with the unprecedented effect of global warming. Knowledge about the spatiotemporal distributions of droughts and their trends is crucial for risk management and developing mitigation strategies. In this study, we developed seven artificial neural network (ANN) predictive models incorporating hydro-meteorological, climate, sea surface temperatures, and topographic attributes to forecast the standardized precipitation evapotranspiration index (SPEI) for seven stations in the Upper Blue Nile basin (UBN) of Ethiopia from 1986 to 2015. The main aim was to analyze the sensitivity of drought-trigger input parameters and to measure their predictive ability by comparing the predicted values with the observed values. Statistical comparisons of the different models showed that accurate results in predicting SPEI values could be achieved by including large-scale climate indices. Furthermore, it was found that the coefficient of determination and the root-mean-square error of the best architecture ranged from 0.820 to 0.949 and 0.263 to 0.428, respectively. In terms of statistical achievement, we concluded that ANNs offer an alternative framework for forecasting the SPEI drought index.