For NAND flash memory, designing a good low-density parity-check (LDPC) decoding algorithm could ensure data reliability. When the decoding algorithm is implemented in hardware, it is necessary to achieve attractive trade off between implementation complexity and decoding performance. In this paper, a novel low bit-width decoding scheme is introduced. In this scheme, the Quasi-Cyclic LDPC (QC-LDPC) is used, and the row-layered normalized min-sum algorithm is improved by restricting the amplitude of minimum and second-minimum values in each check node (CN) updating. The simulation shows that our approach achieves a lower UBER (Uncorrectable Bit Error Rate) with a negligible increase in computational complexity, especially with low precision input log-likelihood ratio (LLR).