In Mobile IPv6 networks, mutual authentication between mobile users and the network guarantees security of both sides. The integration of handoff procedure and authentication procedure may affect performance of the former while improving efficiency of the later. One important issue is to improve the overall efficiency of fast authentication. Based on the Combined Public Key (CPK) algorithm, a new signature and verification scheme is designed, which has a lower computational complexity than identity-based signature (IBS) scheme. Furthermore, a fast authentication method based on this scheme is proposed to realize mutual authentication in one round-trip. Theoretical analysis and numerical results show that the proposed method is more effective in reducing total handoff and authentication delay and the signaling overhead. Security analysis shows that the method is sufficient for privacy and unforgeability.