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This paper is devoted to exploring the mapping properties for the commutator μ_Ω,b generated by multilinear Marcinkiewicz integral operators μ_Ω with a locally integrable function b= (b_1,···,b_m) on the generalized Morrey spaces. μ_Ω,b is bounded from L^(p_1 ,φ_1) (R^n )×···×L^(p_m,φ_m) (R^n) to L ^(q,φ) (R^n), where L^(p_i ,φ_i ) (R^n), L^(q,φ) (R^n) are generalized Morrey spaces with certain variable growth condition, that b_j(j=1,···,m) is a function in generalized Campanato spaces, which contain the BMO(R^n) and the Lipschitz spaces Lip_α(R^n) (0, number=4, journal=Journal of Mathematical Study, year=2023, month=Dec., pages=412–438