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In this paper, we present oblivious transfer with complex attribute-based access control policies. The protocol allows a database server to directly enforce "and" and "or" access control policies (c11 ∧ c12 ∧...c1n1)∨(c21 ∧c22 ∧...c2n2)∨...∨(ct1 ∧ct2∧...ctnt) on each message in a database without duplication of the message as in Camenisch et al.'s AC-OT. To realize this protocol, we present the blind attribute-based encryption (ABE) scheme as a building block. Combining the blind ABE with a credential signature scheme, a generic construction for the oblivious transfer with complicated access control is presented. We also give a concrete scheme for the construction in which the policy is provided by an access tree which is represented by a formula involving "and(∧)" and "or(∨)" boolean operators.