The raw error rate of a Solid-State drive (SSD) increases gradually with the increase of Program/Erase (P/E) cycles, retention time, and read cycles. Traditional approaches often use Error Correction Code (ECC) to ensure the reliability of SSDs. For error-free flash memory pages, time costs spent on ECC are redundant and make read performance suboptimal. This article presents a CRC-Detect-First LDPC (CDF-LDPC) algorithm to optimize the read performance of SSDs. The basic idea is to bypass Low-Density Parity-Check (LDPC) decoding of error-free flash memory pages, which can be found using a Cyclic Redundancy Check (CRC) code. Thus, error-free pages can be read directly without sacrificing the reliability of SSDs. Experiment results show that the read performance is improved more than 50% compared with traditional approaches. In particular, when idle time of benchmarks and SSD parallelism are exploited, CDF-LDPC can be performed more efficiently. In this case, the read performance of SSDs can be improved up to about 80% compared to that of the state-of-art.