In this paper we propose an adaptive modulation and coding (AMC) scheme which uses only a single low-density parity-check (LDPC) encoder/decoder with irregular modulation. Two Gray-mapped quadrature-amplitude modulations are employed within a codeword so that the transmission rates of the proposed AMC can be controlled even though the rate of the employed LDPC code is fixed. The rate and degree distribution of the employed LDPC code are selected properly for the proposed scheme. We also optimize the bit-to-symbol mapping for the LDPC code over irregular modulation at each transmission rate. The performance of the proposed scheme is compared with that of the AMC scheme with a dedicated LDPC code at each transmission rate. Numerical results show that the proposed scheme has a performance comparable to that of the AMC scheme with dedicated LDPC codes.