The multilevel per cell technology and continued scaling down process technology significantly improves the storage density of NAND flash memory but also brings about a challenge in that data reliability degrades due to the serious noise. To ensure the data reliability, many noise mitigation technologies have been proposed. However, they only mitigate one of the noises of the NAND flash memory channel. In this paper, we consider all the main noises and present a novel neural network-assisted error correction (ANNAEC) scheme to increase the reliability of multi-level cell (MLC) NAND flash memory. To avoid using retention time as an input parameter of the neural network, we propose a relative log-likelihood ratio (LLR) to estimate the actual LLR. Then, we transform the bit detection into a clustering problem and propose to employ a neural network to learn the error characteristics of the NAND flash memory channel. Therefore, the trained neural network has optimized performances of bit error detection. Simulation results show that our proposed scheme can significantly improve the performance of the bit error detection and increase the endurance of NAND flash memory.