A new method for detecting and eliminating the Electrocardiogram(ECG) artifact from the scalp Electroencephalogram(EEG) is proposed. Based on the single channel EEG, the proposed method consists of 4 procedures: emphasizing the R-wave of ECG artifact from EEG using the least squares acceleration(LSA) filter, detecting the R-wave from the LSA filtered EEG using the phase space method and R-R interval, generating the delayed impulse synchronized to the R-wave and elimination of the ECG artifacts based on the adaptive digital filter using the impulse and raw EEG. The performance of the proposed method was evaluated in the two separating parts of R-wave detection and, ECG estimation and elimination from EEG. In the R-wave detection, the proposed method showed the mean error rate of 6.285(%). In the ECG estimation and elimination using simulated and/or real EEG recordings, we found that the ECG artifacts were successfully estimated and eliminated in comparison with the conventional multi-channel techniques, in which independent component analysis and ensemble average method are used. From this we can conclude that the proposed method is useful for the detecting and eliminating the ECG artifact from single channel EEG and simple for ambulatory/portable EEG monitoring system.