Two adaptive coded modulation schemes employing LDPC (low-density parity-check) code are proposed for Rayleigh fading channels. Scheme 1: we fix the code rate (rate=1/2), and only change the modulation methods according to the channel state, that is, during poor channel conditions, QPSK modulation is employed, as channel conditions improve, more efficient modulation scheme such as 8PSK is used. Scheme 2: the modulation scheme is fixed (BPSK modulation), and the code rate is changed according to the channel state. Through simulation, we get the performance of these two adaptive LDPC schemes under different demands of BER, and the comparison between adaptive LDPC and nonadaptive LDPC is also given.