This paper proposes a new energy-efficient local metric, termed as efficient advancement metric (EAM), for channel aware geographic-informed forwarding (CAGIF) algorithm, which studies the optimal selection of the relay nodes by taking into account the underlying channel conditions. The proposed metric considers not only the forward distance but also the packet successful probability under a certain channel condition, rather than purely maximizing the forward distance, to choose the most energy-efficient relay node in the geographic- informed routing protocol in a CDMA-based wireless sensor network. The proposed algorithm only requires that nodes have the knowledge of their own location information and the location information of the source and destination nodes. The protocol assumes that nodes could vary transmission range to search for the optimal relay nodes according to this metric. An analytical framework is provided and numerical results show that there exists an optimum distance of a relay node under a certain channel condition to maximize the EAM for any fading conditions.