Multi-authenticated encryption scheme is message transmission scheme, which sends message in a secure and authentic way, and allows a group of signers to cooperatively produce a valid authenticated ciphertext so that only the specific recipient can recover the message and verify the signature. Recently, Wu et al. proposed a convertible multi-authenticated encryption scheme and claimed that the scheme was secure. In this paper, we show that Wu et. al’s scheme is not secure against rogue-key attacks. To overcome such attack, we give an improved multi-authenticated encryption scheme by including two hash functions. And our improved scheme is the same efficiency as Wu et.al.’s scheme.