Fatigue is a major challenge when moving steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs) from the laboratory into real-life applications, as it leads to user's discomfort and system performance degradation. To study and eventually reduce the fatigue, the first step is to know the fatigue level for which a reliable and objective method to the assessment would be very important and helpful. This paper considers the synchronization of brain activities at multiple time scales as such a measure. Specifically, we propose an objective fatigue index based on the multi-scale entropy (MSE) of subjects' electroencephalogram (EEG) and validate it through an experimental study on 12 subjects. Main results show that the proposed fatigue index is significantly correlated with the subjective fatigue index and it can be used to distinguish the 'alert' and 'fatigue' states with 97% accuracy, which is significantly better than the existing fatigue indices based on different EEG spectrum, such as θ, α, and β. The proposed fatigue index would provide an assessment tool for the smart wearable BCI in real-life applications and an ergonomic evaluation method for other human-machine cooperation.