Cryptography is the ancient science of encrypting messages so that only the sender and receiver can recover them. To achieve this goal, an agreed key between the sender and receiver is required. In asymmetric cryptosytems, so far, only a few ID-based key agreement protocols are one-way and most of them can only provide authentication for only one entity to the other. In this paper, two ID-based one-way key agreement protocols are proposed. The advantage of our protocols is that the authentication of the sender and receiver is established at the same time although the key distribution is only one pass. In addition, transmitted data size in our schemes is very small and the parameter for key agreement consists of just one. In this paper, an additional security attribute for key agreement protocols is defined and the rigorous security of our protocols is estimated. The performance evaluation is also analyzed by comparing our schemes with the previous schemes.