Group key agreement (GKA) is a cryptographic primitive allowing two or more users to negotiate a shared session key over public networks. Wu et al. recently introduced the concept of asymmetric GKA that allows a group of users to negotiate a common public key, while each user only needs to hold his/her respective private key. However, Wu et al.'s protocol can not resist active attacks, such as fabrication. To solve this problem, Zhang et al. proposed an authenticated asymmetric GKA protocol, where each user is authenticated during the negotiation process, so it can resist active attacks. Whereas, Zhang et al.'s protocol needs a partially trusted certificate authority to issue certificates, which brings a heavy certificate management burden. To eliminate such cost, Zhang et al. constructed another protocol in identity-based setting. Unfortunately, it suffers from the so-called key escrow problem. In this paper, we propose the certificateless authenticated asymmetric group key agreement protocol which does not have certificate management burden and key escrow problem. Besides, our protocol achieves known-key security, unknown key-share security, key-compromise impersonation security, and key control security. Our simulation based on the pairing-based cryptography (PBC) library shows that this protocol is efficient and practical.