Eye blink is one of the most common artifacts in electroencephalogram (EEG) and significantly affects the performance of the EEG related applications, such as epilepsy recognition, spike detection, encephalitis diagnosis, etc. To achieve an accurate and efficient eye blink detection, a novel unsupervised learning algorithm based on a hybrid thresholding followed with a Gaussian mixture model (GMM) is presented in this paper. The EEG signal is priliminarily screened by a cascaded thresholding method built on the distributions of signal amplitude, amplitude displacement, as well as the cross channel correlation. Then, the channel correlation of the two frontal electrodes (FP1, FP2), the fractal dimension, and the mean of amplitude difference between FP1 and FP2, are extracted to characterize the filtered EEGs. The GMM trained on these features is applied for the eye blink detection. The performance of the proposed algorithm is studied on two EEG datasets collected by the Temple University Hospital (TUH) and the Children's Hospital, Zhejiang University School of Medicine (CHZU), where the datasets are recorded from epilepsy and encephalitis patients, and contain a lot of eye blink artifacts. Experimental results show that the proposed algorithm can achieve the highest detection precision and F1 score over the state-of-the-art methods.