Objective: Recent advances in development of low-cost single-channel electroencephalography (EEG) headbands have opened new possibilities for applications in health monitoring and brain-computer interface (BCI) systems. These recorded EEG signals, however, are often contaminated by eye blink artifacts that can yield the fallacious interpretation of the brain activity. This paper proposes an efficient algorithm, VME-DWT, to remove eye blinks in a short segment of the single EEG channel. Method: The proposed algorithm: (a) locates eye blink intervals using Variational Mode Extraction (VME) and (b) filters only contaminated EEG interval using an automatic Discrete Wavelet Transform (DWT) algorithm. The performance of VME-DWT is compared with an automatic Variational Mode Decomposition (AVMD) and a DWT-based algorithms, proposed for suppressing eye blinks in a short segment of the single EEG channel. Results: The VME-DWT detects and filters 95% of the eye blinks from the contaminated EEG signals with SNR ranging from -8 to +3 dB. The VME-DWT shows superiority to the AVMD and DWT with the higher mean value of correlation coefficient (0.92 vs. 0.83, 0.58) and lower mean value of RRMSE (0.42 vs. 0.59, 0.87). Significance: The VME-DWT can be a suitable algorithm for removal of eye blinks in low-cost single-channel EEG systems as it is: (a) computationally-efficient, the contaminated EEG signal is filtered in millisecond time resolution, (b) automatic, no human intervention is required, (c) low-invasive, EEG intervals without contamination remained unaltered, and (d) low-complexity, without need to the artifact reference.