In this paper, a novel adaptive noise canceller (ANC) based on the quaternion valued least mean square algorithm (QLMS) is designed in order to remove electrooculography (EOG) artifacts from electroencephalography (EEG) recordings. The measurement real-valued EOG and EEG signals (FP1, FP2, AF3 and AF4) are first modeled as four-dimensional processes in the quaternion domain. The EOG artifacts are then removed from the EEG signals in the quaternion domain by using the ANC based on QLMS algorithm. The quaternion representation of these signals allows us to remove EOG artifacts from all channels at the same time instead of removing the EOG artifacts in each EEG recordings separately. The simulation results support the proposed approach.