Summary: The restarted global CMRH method (Gl-CMRH\((m)\)) [M. Heyouni, Numer. Algorithms 26, No. 4, 317–332 (2001; Zbl 0979.65025)] is an attractive method for linear systems with multiple right-hand sides. However, Gl-CMRH\((m)\) may converge slowly or even stagnate due to a limited Krylov subspace. To ameliorate this drawback, a polynomial preconditioned variant of Gl-CMRH\((m)\) is presented. We give a theoretical result for the square case that assures that the number of restarts can be reduced with increasing values of the polynomial degree. Numerical experiments from real applications are used to validate the effectiveness of the proposed method.