This work proposes a new direction in quantum cryptography called quantum authencryption. Quantum authencryption (QA), a new term to distinguish from authenticated quantum secure direct communications, is used to describe the technique of combining quantum encryption and quantum authentication into one process for off-line communicants. QA provides a new way of quantum communications without the presence of a receiver on line, and thus makes many applications depending on secure one-way quantum communications, such as quantum E-mail systems, possible. An example protocol using single photons and one-way hash functions is presented to realize the requirements on QA.