In wireless networks, cooperative diversity transmission can considerably improve the reliability of the wireless links with the introduction of a relay node forwarding the source information to the destination. Generally, cooperative system with multiple L relays suffers from a spectral efficiency loss with the factor 1/(L+1), because the transmission process takes place in (L+1) orthogonal channels by using time-division multiple access. To overcome such a spectral efficiency loss, the incremental relaying (IR) scheme for one relay environment was proposed in . In , the incremental opportunistic relaying (IOR) scheme was proposed to extend the IR scheme in conjunction with the best relay selection scheme over multiple relays environment. An alternative approach to improve a spectral efficiency is that all the relays simultaneously transmit on the same subchannel. The relays can share the same bandwidth, and the destination can coherently combine the signals by co-phasing. In addition, adaptive modulation can achieve high spectral efficiency over fading channels while satisfying a certain bit error rate (BER) requirement. The IR with adaptive modulation (IR-AM) scheme was proposed and studied for three-node cooperative transmission system . However, the IR-AM scheme may suffer from some loss of the overall spectral efficiency as it will still use the direct transmission even though the relaying transmission may achieve much higher spectral efficiency. In this paper, we propose a new cooperative transmission scheme for amplify-and-forward (AF) relaying system with multiple relays, termed as maximum spectral efficiency with adaptive modulation (MSE-AM) scheme as its objective is to maximize the spectral efficiency. To accurately quantify the performance gain of the proposed scheme, we carry out accurate analysis on the average spectral efficiency of the MSE-AM scheme based on an upper bound of the combined output signal-to-noise ratio (SNR) with AF relaying. We obtain some useful closed-form expression for some interest cases. Our numerical results show the proposed scheme can offer significant performance gain over the conventional schemes.