In this paper, it is demonstrated that the logic tool used in agent formalized d epiction should be the mixed modal logic which has both normal and non-normal m odal operators. Then a logic system A-BI is built for Agent-BDI logic and its semantics and axiom system are discussed. Especially for non-normal modal opera tors a new semantic interpretation based on Kripke's normal possible worlds is p resented. It is proved that A-BI logic system is sound and complete. A-BI logi c appropriately depicts the essence and relation of belief and intension, and ca n be used as logic tool in formalized research on agent.