In order to build a reliable index to monitor the depth of anesthesia (DOA), many algorithms have been proposed in recent years, one of which is sample entropy (SampEn), a commonly used and important tool to measure the regularity of data series. However, SampEn only estimates the complexity of signals on one time scale. In this study, a new approach is introduced using multiscale entropy (MSE) considering the structure information over different time scales. The entropy values over different time scales calculated through MSE are applied as the input data to train an artificial neural network (ANN) model using bispectral index (BIS) or expert assessment of conscious level (EACL) as the target. To test the performance of the new index's sensitivity to artifacts, we compared the results before and after filtration by multivariate empirical mode decomposition (MEMD). The new approach via ANN is utilized in real EEG signals collected from 26 patients before and after filtering by MEMD, respectively; the results show that is a higher correlation between index from the proposed approach and the gold standard compared with SampEn. Moreover, the proposed approach is more structurally robust to noise and artifacts which indicates that it can be used for monitoring the DOA more accurately.