In special application scenarios, such as portable anesthesia depth monitoring, portable emotional state recognition and portable sleep monitoring, electroencephalogram (EEG) signal acquisition equipment is required to be convenient and easy to use. It is difficult to remove electrooculogram (EOG) artifacts when the number of EEG acquisition channels is small, especially when the number of observed signals is less than that of the source signals, and the overcomplete problem will arise. The independent component analysis (ICA) algorithm commonly used for artifact removal requires the number of basis vectors to be smaller than the dimension of the input data due to a set of standard orthonormal bases learned during the convergence process, so it cannot be used to solve the overcomplete problem. The empirical mode decomposition method decomposes the signal into several independent intrinsic mode functions so that the number of observed signals is more than that of the source signals, solving the overcomplete problem. However, when using this method to solve overcompleteness, the modal aliasing problem will arise, which is caused by abnormal events such as sharp signals, impulse interference, and noise. Aiming at the above problems, we propose a novel EEG artifact removal method based on discrete wavelet transform, complete empirical mode decomposition for adaptive noise (CEEMDAN) and ICA in this paper. First, the input signals are transformed by discrete wavelet (DWT), and then CEEMDAN is used to solve the overcomplete and mode aliasing problems, meeting the a priori conditions of the ICA algorithm. Finally, the components belonging to EOG artifacts are removed according to the sample entropy value of each independent component. Experiments show that this method can effectively remove EOG artifacts while solving the overcomplete and modal aliasing problems.