Mind-wandering (MW), which usually defined as a lapse of attention, occurs between 20%-40% of the time, has negative effects on our daily life. Therefore, detecting when MW occurs can prevent us from those negative outcomes resulting from MW, such as failing to keep track of course during learning. In this work, we first collect a multi-modal Sustained Attention to Response Task (MM-SART) database for detecting MW. Eighty-two participants' data are collected in our experiments. For each participant, we collect measures of 32-channels electroencephalogram (EEG) signals, photoplethysmography (PPG) signals, galvanic skin response (GSR) signals, eye tracker signals, and several questionnaires for detailed analyses. Then, we propose an effective MW detection system based on the collected EEG signals. To explore the non-linear characteristics of EEG signals, we utilize the entropy-based features in time, frequency, and wavelet domains. The experimental results show that we can reach 0.712 AUC score by using the random forest (RF) classifier with the leave-one-subject-out cross-validation. Moreover, to lower the overall computational complexity of the MW detection system, we apply techniques of channel selection and feature selection. By using the only two most significant EEG channels, we can reduce the training time of the classifier by 44.16%. By performing correlation importance feature elimination (CIFE) on the feature set, we can further improve the AUC score to 0.725 but with only 14.6% of the selection time compared with the recursive feature elimination (RFE) method. By proposing the MW detection engine, current work can be applied to educational scenarios, especially in the era of remote learning nowadays.