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The Traditional Authenticated Encryption (AE) scheme is a single-user cryptographic mechanism which only enables one designated verifier to authenticate the ciphertext. Although several group-oriented AE variants have also been proposed to eliminate such a limitation, they require shared verification. This motivated us to think of a scenario of three-party communication environments where each party runs independent processes without cooperation. In this paper, we realize a novel three-party AE (abbreviated to TPAE) scheme in which two designated verifiers can solely decrypt the same ciphertext and then inspect the validity of embedded signature. Additionally, we also show that our TPAE construction is computationally secure using the well-defined IND-CCA2 and the EF-CMA adversary games in the proof model of random oracles. The comparison results will demonstrate the computational efficiency of our mechanism.