The reliable monitoring of the depth of anesthesia (DoA) is essential to control the anesthesia procedure. Electroencephalography (EEG) has been widely used to estimate DoA since EEG could reflect the effect of anesthetic drugs on the central nervous system (CNS). In this study, we propose that a deep learning model consisting mainly of a deep residual shrinkage network (DRSN) and a 1 × 1 convolution network could estimate DoA in terms of patient state index (PSI) values. First, we preprocessed the four raw channels of EEG signals to remove electrical noise and other physiological signals. The proposed model then takes the preprocessed EEG signals as inputs to predict PSI values. Then we extracted 14 features from the preprocessed EEG signals and implemented three conventional feature-based models as comparisons. A dataset of 18 patients was used to evaluate the models’ performances. The results of the five-fold cross-validation show that there is a relatively high similarity between the ground-truth PSI values and the predicted PSI values of our proposed model, which outperforms the conventional models, and further, that the Spearman’s rank correlation coefficient is 0.9344. In addition, an ablation experiment was conducted to demonstrate the effectiveness of the soft-thresholding module for EEG-signal processing, and a cross-subject validation was implemented to illustrate the robustness of the proposed method. In summary, the procedure is not merely feasible for estimating DoA by mimicking PSI values but also inspired us to develop a precise DoA-estimation system with more convincing assessments of anesthetization levels.