In this paper, an entropy based method for quantifying the depth of anesthesia from rat EEG is presented. The proposed index for the depth of anesthesia called modified Shannon entropy (MShEn) is based on Shannon entropy (ShEn) and spectral entropy (SpEn) which are widely used for analyzing non-stationary signals. Discrimination power (DP), as a performance indicator for indexes, is defined and used to derive the final index for the depth of anesthesia. For experiment, EEG from anesthetized rats are measured and analyzed by using MShEn. MShEn shows both high stability and high correlation with other indexes for depth of anesthesia.