In this paper, a novel extended form of multivariate variational mode decomposition (MVMD) method to multigroup data named as grouped MVMD (GMVMD) is proposed. GMVMD is distinct from MVMD as it extracts common frequencies with strong correlations among regional channels.Firstly, GMVMD utilizes a new clustering algorithm named as frequencies grouping algorithm to classify the nearest common frequencies among all channels to specified groups. Secondly, a generic variational optimization model which is extended from MVMD is formulated. Thirdly, alternating direction method of multipliers (ADMM) is utilized to obtain optimal solution of GMVMD model.The proposed method introduces an extra parameter to decide the number of clusterings which need to be specified by the user. The effectiveness and superiority of the algorithm are demonstrated on a series of experiments. The utility of GMVMD is verified by grouping real-world electroencephalogram (EEG) data having similar center frequencies successfully.GMVMD outperforms MVMD in mode-alignment, signal reduction error and et al. Significance: GMVMD can obtain more accurate center frequencies and less signal reduction error than MVMD.