The Reliability-Based Hybrid ARQ (RB-HARQ) scheme, which can be used with error correcting codes using soft-input soft-output (SISO) decoders such as convolutional codes and turbo codes has been proposed. In the RB-HARQ scheme, the error rate performance is improved by selecting the retransmission bits based on Log Likelihood Ratio (LLR) of each bit in the receiver. However, the receiver has to send the bit positions of retransmission bits to the transmitter. Therefore, the RB-HARQ scheme requires a great number of feedback bits. On the other hand, Low Density Parity Check (LDPC) codes are attracting a lot of interest, recently. Because LDPC codes can achieve near Shannon limit performance and be decoded easily compared to turbo code. In this paper, we evaluate the RB-HARQ scheme using LDPC code. Moreover, we propose a RB-HARQ scheme that requires a fewer feedback bits by utilizing a code structure of LDPC code. We refer to the scheme as the RB-HARQ (row base) scheme. We show that the RB-HARQ and RB-HARQ (row base) schemes using LDPC code have better error rate performance than the scheme without ARQ. We also show that the RB-HARQ (row base) scheme has a good trade-off between error rate performance and the number of feedback bits compared to the RB-HARQ scheme.