In this paper,some weighted estimates with general weights are established for the m-linear Calderón-Zygmund operator and the corresponding maximal operator.It is proved that,if P1,…,Pm ∈ [1,∞]and p ∈ (0,∞) with l/p =mΣk=1 1/pk,then for any weight w,integer e with 1 ≤ e ≤ m,these operators are bounded from Lp1 ((R)n,MBw) ×… × Lpe ((R)n,MBw) × Lpe+1 ((R)n,Mw) ×… × Lpm ((R)n,Mw) to Lp,∞ ((R)n,w) or Lp((R)n,w),where B is a Young function and MB is the maximal operator associated with B.