These day many research have demonstrated that the EEG possesses long term correlation in the dynamics of broad band oscillations. The DFA(detrended fluctuation analysis) is used to quantify the fractal-like scaling properties of the EEG. In this paper, we have used the DFA method to estimate the depth of anesthesia. The power-law exponent of DFA (detrended fluctuation analysis) of the brain waves during surgeries was used to measure the depth of anesthesia. We studied 12 ASA I or II adult patients. Patients with history of dementia and neurological disorder are excluded. EEG data, obtained from 9 patients, was used to experiment. The data was obtained for 10 minutes one day before the surgery and from the stage of injecting the anesthesia in the surgery room, up to the stage of anesthesia suspension and the recovery of the patient, and the data was obtained for 10 minutes one day after the surgery. We analyzed with detrended fluctuation analysis (DFA), a scaling analysis method that quantifies a slope of the result of DFA to represent the correlation properties of a time series. The scaling exponent, the result of DFA, provides a quantitative measure of correlation from the EEG. Among the scaling exponent alpha 1, alpha 2 and alpha 3, we know that, alpha 1 and alpha 3 were well appeared to discriminate the depth of anesthesia. And these parameters as useful indicators of depth of anesthesia may be used are expected.