Treating an averaged evoked-fields (EFs) or event-related potentials (ERPs) data is a main approach in the topics on applying Independent Component Analysis (ICA) to neurobiological signal processing. By taking the average, the signal-noise ratio (SNR) is increased, however some important information such as the strength of an evoked response and its dynamics (trial-by-trial variations) will be lost. The single-trial data analysis, on the other hand, can avoid this problem but the poor SNR is necessary to be improved. This paper presents a robust multi-stage data analysis method for the single-trial Magnetoencephalograph (MEG) and Electroencephalograph (EEG) recorded data. In the pre-processing stage, a robust subspace method is firstly applied for reducing a high-level unique component (additive noise) in single-trial raw data. In the second stage, a parameterized t-distribution ICA method is applied for further decomposing the overlapped common components (sources). In the post-processing stage, the source localization or scalp mapping technique and post-averaging technique are applied for visualizing the dynamic brain activities. The results on single-trial MEG and EEG data analysis both illustrate the high performances not only in the visualization of the behavior and location but also in the visualization of the trial-by-trial variations of individual evoked brain response.