2-time slot cooperative relay can be used to increase the cell-edge throughput. Adaptive data modulation further improves the throughput. In this paper, we introduce adaptive modulation to single-carrier (SC) cooperative decode-and-forward (DF) relay. The best modulation combination for mobile-terminal (MT)-relay station (RS) and RS-base station (BS) links is determined for the given local average signal-to-noise power ratios (SNRs) of MT-BS, MT-RS and RS-BS links. According to the modulation combination, the ratio of time slot length of the MT-RS link (first time slot) and the RS-BS link (second time slot) is changed. It is shown by computer simulation that the use of adaptive modulation can achieve higher throughput than fixed modulation and reduces by about 9dB the required normalized total transmit SNR for a 10%-outage throughput of 0.8 bps/Hz compared to direct transmission.