Organ motion is a major challenge in the radiation treatment of lung and abdominal cancers, which, if unaccounted for, may lead to the underdosing of cancer cells or overdosing of normal tissue, potentially causing treatment failure or normaltissue toxicity. Recent developments in the field of radiation therapy have allowed for a real-time depiction of organ motion through MRI imaging to guide the radiation delivery process. The goal of this research is to develop and test artificial neural network (ANN) models to predict the future trajectory of anatomical motion during treatment. We employ image-processing tools to extract a one-dimensional signal from the sequence of acquired MRI images to describe the anatomical motion. We develop and train ANN models to predict the signal amplitude at future time points using the Neural Net Time Series toolbox in MATLAB. Using different prediction horizons, we apply the proposed ANN model retrospectively to de-identified cancer patients and compare the prediction accuracy against other autoregressive models for time-series prediction. The obtained results show that the ANN model outperforms linear autoregressive model.