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Human electroencephalography (EEG) is a brain monitoring modality that senses cortical neuroelectrophysiological activity in high-temporal resolution. One of the greatest challenges posed in applications of EEG is the unstable signal quality susceptible to inevitable artifacts during recordings. To date, most existing techniques for EEG artifact removal and reconstruction are applicable to offline analysis solely, or require individualized training data to facilitate online reconstruction. We have proposed CLEEGN, a novel convolutional neural network for plug-and-play automatic EEG reconstruction. CLEEGN is based on a subject-independent pre-trained model using existing data and can operate on a new user without any further calibration. The performance of CLEEGN was validated using multiple evaluations including waveform observation, reconstruction error assessment, and decoding accuracy on well-studied labeled datasets. The results of simulated online validation suggest that, even without any calibration, CLEEGN can largely preserve inherent brain activity and outperforms leading online/offline artifact removal methods in the decoding accuracy of reconstructed EEG data. In addition, visualization of model parameters and latent features exhibit the model behavior and reveal explainable insights related to existing knowledge of neuroscience. We foresee pervasive applications of CLEEGN in prospective works of online plug-and-play EEG decoding and analysis.