The concatenation scheme of low-density parity-check (LDPC) codes and space-time block coding (LDPC-STBC) has been proved to be effective in the multiple-input multiple-output (MIMO) system. In this paper, we extend the LDPC-STBC to the distributed communication system with non-regenerative relays. Two LDPC coded distributed space-time cooperative (LDPC-DSTC) schemes are proposed, which utilize different signal combination methods at the destination. The decoding algorithms are discussed. The performance of these proposed schemes is examined in wireless communication systems with one and two relays. Simulation results show that both of the proposed LDPC-DSTC schemes reduce the transmission error and offer the diversity gain, and that the location of the relays has profound impact on the system performance.