In this paper, we propose a RB-SR-HARQ (Selective Repeat Based on Reliability) protocol on Low Density Parity Check codes, which exploits the estimated bits reliabilities at the output of a decoder to retransmit those unreliable bits. Our scheme improves system performance and minimizes retransmission sizes by only retransmitting those bits which are likely to be in error. We simulate RB-SR-HARQ protocol on Low Density Parity Check codes both over AWGN and Rayleigh flat-fading channel. At the same time, we also compare our proposed RB-SR-HARQ protocol with IR (incremental redundancy) HARQ protocol on LDPC codes. The results show that our proposed scheme achieves a lower BER than other schemes both over AWGN and Rayleigh flat-fading channel.