The intermediate logic is a three-valued logic proposed by Zhu Wu-Jia. A propositional intermediate logic is proposed in this paper where the intermediate unary connective ~ and the contrary connective ◁ are introduced, and the negative connective ¬ is defined in terms of the unique binary connective →. A Gentzen-typed deduction system is given such that the system is sound and complete with the three-valued semantics of the propositional intermediate logic.