Alzheimer's disease (AD) is the most common cause of dementia and threatens the health of millions of people. Early stage diagnosis of AD is critical for improving clinical outcomes and longitudinal magnetic resonance imaging (MRI) data collection can be used to monitor the progress of each patient. However, missing data is a common problem in longitudinal AD studies. The main factors come from subject dropouts and failed scans. This hinders the acquisition of longitudinal sequences that consist of multi-time-point magnetic resonance (MR) images at relatively uniform intervals. In this paper, we present a generative adversarial convolutional network to predict missing structural MRI data. In particular, we include multiple MRI scans as a temporal sequence collected at different times and determine the spatio-temporal relationship between the different scans in the proposed network. We adopt residual bottlenecks in the generator to decrease parameter values and deepen the network. In order to make full use of the longitudinal information, our discriminator classifies not only real MR images from generated MR images, but also fake sequences from real sequences in which the longitudinal MR images for all time points come from the dataset, only the last MR image comes from the generator. Results of our experiment show that our method performs more accurately for the longitudinal structural MRI data prediction of a brain afflicted with AD.