A potential limitation of a motor imagery (MI) based brain-computer interface (BCI) is that it usually requires a relatively long time to record sufficient electroencephalogram (EEG) data for robust classifier training. The calibration burden during data acquisition phase will most probably cause a subject to be reluctant to use a BCI system. To alleviate this issue, we propose a novel sparse group representation model (SGRM) for improving the efficiency of MI-based BCI by exploiting the intersubject information. Specifically, preceded by feature extraction using common spatial pattern, a composite dictionary matrix is constructed with training samples from both the target subject and other subjects. By explicitly exploiting within-group sparse and group-wise sparse constraints, the most compact representation of a test sample of the target subject is then estimated as a linear combination of columns in the dictionary matrix. Classification is implemented by calculating the class-specific representation residual based on the significant training samples corresponding to the nonzero representation coefficients. Accordingly, the proposed SGRM method effectively reduces the required training samples from the target subject due to auxiliary data available from other subjects. With two public EEG data sets, extensive experimental comparisons are carried out between SGRM and other state-of-the-art approaches. Superior classification performance of our method using 40 trials of the target subject for model calibration (Averaged accuracy = 78.2%, Kappa = 0.57 and Averaged accuracy = 77.7%, Kappa = 0.55 for the two data sets, respectively) indicates its promising potential for improving the practicality of MI-based BCI.