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We consider linear regression problems for which the underlying model undergoes multiple changes. Our goal is to estimate the number and locations of change-points that segment available data into different regions, and further produce sparse and interpretable models for each region. To address challenges of the existing approaches and to produce interpretable models, we propose a sparse group Lasso based approach for linear regression problems with change-points. Under certain mild assumptions and a properly chosen regularization term, we prove that the solution of the proposed approach is asymptotically consistent. In particular, we show that the estimation error of linear coefficients diminishes, and the locations of the estimated change-points are close to those of true change-points. We further propose a method to choose the regularization term so that the results mentioned above hold. In addition, we show that the complexity of the proposed algorithm is much smaller than those of existing approaches. Numerical examples are provided to validate the analytical results. [ABSTRACT FROM PUBLISHER]