To achieve security in the networks, it is important to be able to encrypt and authenticate messages sent between the users. Keys for encryption and authentication purposes must be agreed upon by the users in the networks. Three new pairwise key agreement protocols based on Weil pairing are proposed in this paper. In those protocols, all the users share common secret information. They may arrange the pairwise key and authenticate each other by fewer messages. The proposed protocols have the security attributes such as known session key security, perfect forward secrecy, no key-compromise impersonation, no unknown key-share and no key control.