Understanding brain dynamics is important for neuroscience and mental health. Functional magnetic resonance imaging (fMRI) enables the measurement of neural activities through blood-oxygen-level-dependent (BOLD) signals, which represent brain states. In this study, we aim to predict future human resting brain states with fMRI. Due to the 3D voxel-wise spatial organization and temporal dependencies of the fMRI data, we propose a novel architecture which employs a 4D Shifted Window (Swin) Transformer as encoder to efficiently learn spatio-temporal information and a convolutional decoder to enable brain state prediction at the same spatial and temporal resolution as the input fMRI data. We used 100 unrelated subjects from the Human Connectome Project (HCP) for model training and testing. Our novel model has shown high accuracy when predicting 7.2s resting-state brain activities based on the prior 23.04s fMRI time series. The predicted brain states highly resemble BOLD contrast and dynamics. This work shows promising evidence that the spatiotemporal organization of the human brain can be learned by a Swin Transformer model, at high resolution, which provides a potential for reducing the fMRI scan time and the development of brain-computer interfaces in the future.