Abstract: Due to the time-varying wireless channel and the lack of wireless spectrum resource, code-rate adaption technique and high order modulation scheme with high spectrum efficiency will be the most attractive candidates for high speed wireless communication in future. In this paper, a variable--rate high order modulation scheme based on non-binary rate-compatible low-density parity-check (RC-LDPC）codes was proposed. In this scheme, the symbol-wise shortening algorithm and puncturing algorithm for non-binary LDPC codes were provided, and the jointed design of high order mapping and non-binary RC-LDPC codes were proposed, too. With these algorithms, some information bits or redundancy bits will be not transmitted over wireless channels; at the receiver, the partial code-words should be filled with some proper bits or probabilities. Finally, we can obtain a non-binary RC-LDPC-coded high order modulation scheme with the flexible code-rate range from 1/3 to 5/6. And all rate-compatible LDPC codes can be decoded by using the parity-check matrix of the mother code, so the complexity will not increase significantly. Finally, simulation results show that gains of 0.51-1.3dB are obtained over binary RC-LDPC-coded 64-QAM-modulation schemes.