In definition, let Φ be a non negative locally integral function on Rⁿ and satisfy weak growth condition, and A be a function on Rⁿ with derivatives of order one in BMO(Rⁿ). Considering the multi linear potential type integral operator T^A_Φ generated by Φ and A, this paper discusses the weighted inequalities of arbitrary weight for T^A_Φ associated with its maximal function.