Early identification of individuals at risk of developing Alzheimer's disease (AD) dementia is important for developing disease-modifying therapies. In this study, given multimodal AD markers and clinical diagnosis of an individual from one or more timepoints, we seek to predict the clinical diagnosis, cognition and ventricular volume of the individual for every month (indefinitely) into the future. We proposed a recurrent neural network (RNN) model and applied it to data from The Alzheimer's Disease Prediction Of Longitudinal Evolution (TADPOLE) challenge, comprising longitudinal data of 1677 participants (Marinescu et al. 2018) from the Alzheimer's Disease Neuroimaging Initiative (ADNI). We compared the performance of the RNN model and three baseline algorithms up to 6 years into the future.Most previous work on predicting AD progression ignore the issue of missing data, which is a prevalent issue in longitudinal data. Here, we explored three different strategies to handle missing data. Two of the strategies treated the missing data as a "preprocessing" issue, by imputing the missing data using the previous timepoint ("forward filling") or linear interpolation ("linear filling). The third strategy utilized the RNN model itself to fill in the missing data both during training and testing ("model filling"). Our analyses suggest that the RNN with "model filling" was better than baseline algorithms, including support vector machine/regression and linear state space (LSS) models. However, there was no statistical difference between the RNN and LSS for predicting cognition and ventricular volume.Importantly, although the training procedure utilized longitudinal data, we found that the trained RNN model exhibited similar performance, when using only 1 input timepoint or 4 input timepoints, suggesting that our approach might work well with just cross-sectional data.An earlier version of our approach was ranked 5th (out of 53 entries) in the TADPOLE challenge in 2019. The current approach is ranked 2nd out of 56 entries as of August 12th, 2019.