For the large-scale linear discrete ill-posed problems with multiple right-hand sides, the global Krylov subspace iterative methods have received a lot of attention. In this paper, we analyze the regularizing properties of the global generalized minimum error method (GMERR), and develop a regularized global GMERR method for solving linear discrete ill-posed problems with multiple right-hand sides. The efficiency of the proposed method is confirmed by the numerical experiments on test matrices.