A deterministic secure quantum communication (DSQC) scheme with mutual authentication is proposed, where unitary operations are not necessary, while they are indispensable in other quantum direct communication (QDC) schemes. Since the realization of a unitary operation is not a simple task in quantum computation and quantum communication, it simplifies the implementation of QDC schemes to a great extent. The scheme is partitioned into two parts, mutual authentication and direct communication. To authenticate identities of the two users, an authentication strategy is put forward by utilizing the property of Bell states in which unitary is not performed. In direct communication phase, Alice and Bob can communicate directly and deterministically without any unitary operation due to the property of entanglement swapping. Naturally, the security of the presented DSQC scheme is discussed in detail. Compared with the previous QDC protocols, the proposed DSQC scheme has some meaningful advantages.