With advantages of high concealment, non-stealing, and liveness detection, electroencephalography (EEG) identification has a broad application prospect in the fields with high confidentiality and security requirements. At present, EEG identification usually requires external stimuli or particular tasks imposed on participators, such as identification based on movement imagination (MI) and event-related potential (ERP), which restricts its promotion in real life. To overcome the limitation, we assume a task-related EEG can be divided into a background EEG (BEEG) containing one's unique intrinsic features and a residue EEG (REEG) composed of task-evoked EEG and random noise. Furthermore, we suppose only a few features can reveal one's identity. Therefore, BEEG represents a low-rank characteristic, suitable for personal identification. In this paper, we proposed a fast LRMD-based EEG identification algorithm with maximum correntropy criterion (MCC) and rational quadratic kernel, which can efficiently extract BEEG out and deliver a high accuracy classification. Extensive experiments conducted on three public EEG datasets and a self-collected multi-task EEG dataset all achieve outstanding performance under the low rank of BEEG data matrix and various time length scales of short-time Fourier Transform (STFT), which means that our approach does not depend on the task type. Besides, the experimental results provide a reference for the time length of an appropriate EEG signal sample.