Abstract: In this paper, high-order adaptive coded modulation (ACM) schemes based on non-binary rate-compatible (RC) LDPC codes over GF(q) were designed. Further, the incremental redundancy schemes of non-binary RC-LDPC-based ACM system over independent and correlative fading channels were proposed. In the proposed schemes, the LDPC encoder can provide a flexible code-rate range from 1/3 to 5/6 by shortening and puncturing algorithm. And the proposed schemes can improve the spectrum efficiency of system with little extra complexity. Simulations show that, with higher throughput rate, much more visible even 9 dB coding gain can be obtained by proposed non-binary ACM system than binary system.