In this paper, we consider adaptive quadratic amplitude modulation (QAM) for a cooperative network consists of a source, one decode-and-forward (DF) relay and a destination which are single antenna systems. For increasing the spectral efficiency of the system, we use adaptive modulation method for data transmission. We propose a new adaptive modulation scheme which has less complexity than available schemes. Then, we analyze average spectral efficiency (ASE), average bit error performance (ABEP) and outage probability of the proposed scheme. Computer simulation results corroborate our theoretical relations; furthermore, it shows that our proposed scheme has the same performance as maximum spectral efficiency scheme (MSES) with much lower complexity and has better performance than some other schemes.