Adaptive modulation techniques can improve the BER (bit error rate) performance or the average throughput by employing a suitable modulation mode depending on the instantaneous channel SNR (signal-to-noise ridio). In this paper the optimum SNR thresholds over a 6-path Rayleigh channel are derived, which shows a superior BPS (bit per symbol) throughput performance while maintaining the target average BER. The 6-path Rayleigh channel is often applied to mobile environment with high-speed. The results achieved in this paper can be applied to the adaptive modulation system with the channel of ITU-R M. 1225 Vehicular Test A mode.