The mechanism of prediction is necessary for realizing human smooth pursuit eye movements. Some cortical regions are well known for contributing to realize it, but it is not clear yet how the brain represents the spatial-temporal information for the eye movements. To answer such question, we measured MEG data during overt/covert pursuit tasks. Subjects were required to overtly or covertly pursue the target motion, that moves in the horizontal plane. Target motions were sinusoidal, and their frequencies were 0.5Hz and 0.8Hz. The cortical currents were estimated using a hierarchical Bayesian MEG inverse method (VBMEG), and investigated the spatial-temporal pattern of the currents. In order to remove the eye and heart-beat artifacts, we used extra-dipole method, which is based on hierarchical Bayesian method and simultaneously estimates the cortical and extra-brain source currents while placing dipoles not only on cortical surfaces but also on extra-brain sources. The intensities of estimated cortical currents during all tasks were increased in the cortical regions of the lateral occipital temporal cortex (LOTC), the intraparietal cortex (IPC), the precentral cortex (PreCC), and the medial superior frontal cortex (MSFC). These areas are related to the saccadic and smooth pursuit eye movements, and also activated when subjects orient their attention to visually target motion and pursue it covertly within their visual fields. We reconstructed the target velocities from the estimated cortical currents using a sparse regression method. Test datasets demonstrated a good performance, and weight values were mainly distributed on the LOTC. These results indicated that this cortical area plays a major role for realizing overt/covert pursuit tasks to represent the spatial-temporal information of the target velocities.