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Let L =-Δ+V(x) be a Schr(o)dinger operator,where Δ is the Laplacian on Rn,while nonnegative potential V(x) belonging to the reverse H(o)lder class.The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kel associated with Schr(o)dinger operator and their commutators.Moreover,the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kel associated with Schr(o)dinger operators is discussed on the generalized weighted Morrey spaces.As its special cases,the corresponding results of Marcinkiewicz integrals with rough kel associated with Schr(o)dinger operator and their commutators have been deduced,respectively.Also,Marcinkiewicz integral operators,rough Hardy-Littlewood (H-L for short) maximal operators,Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.