Low-density parity-check (LDPC) codes are playing more and more important role in digital broadcasting standards due to their excellent error correction performance. In this paper, we study the combination of LDPC codes over GF(q) with q-ary modulations for bandwidth efficient transmission over AWGN channel and consider the design of the codes. Specifically, we develop the concept of quasi-regular codes, and propose an improved Monte Carlo method to optimize the quasi-regular codes. To justify the performance of our proposed scheme, simulation results are presented and analysed.