We introduce a new low-density parity-check (LDPC) decoding algorithm that exploits the cyclic redundancy check (CRC) information of data segments. By using the error detection property of the CRC, we can successively decode data segments of a codeword corrupted by random errors and erasures. The key idea is that the messages from the variable nodes with correct checksum are fixed to deterministic log likelihood ratio values during LDPC iterative decoding. This approach improves the decoding speed and codeword error rate without significant modification of the LDPC decoding structure. Moreover, the CRC is also used for an early stopping criterion of LDPC decoding. Simulation results verify our claims.