Abstract: By using the function decomposition and the inequality technique, with the aid of the theory of boundedness for generalized fractional integral operator commutators on the L^p spaces, the author discussed the boundedness of the commutator T_σ,b generated by the generalized fractional integral operator T_σ and the Lipschitz function b on non-homogeneous metric measure spaces. The results show  that the  T_σ,b is bounded from Morrey spaces M^p1_q1(μ) to M^p2_q2(μ), and also bounded from Morrey spaces M^p_q(μ) to RBMO(μ) spaces.

Key words: non-homogeneous metric measure space, Morrey space, generalized fractional integral operator, commutator