This paper proposes a real-time method to eliminate eye-movement artifacts from frontal electroencephalography (EEG) signals using the total variation de-nosing algorithm. The proposed method is aimed to estimate electrooculography (EOG) artifacts from the EEG signals recorded from the frontal cortical areas using the total variation de-nosing algorithm. Then, it removes the estimated EOG artifacts in real time using a linear adaptive filter trained by the least-mean squares (LMS) algorithm. We demonstrate that our method can effectively remove the EOG artifact from the experimental EEG data. The proposed method may be used for various real-time applications such as non-invasive brain-computer interfaces.