We propose a designing of multi-layer neural networks using 2D NAND flash memory cell as a high-density and reliable synaptic device. Our operation scheme eliminates the waste of NAND flash cells and allows analogue input values. A 3-layer perceptron network with 40,545 synapses is trained on a MNIST database set using an adaptive weight update method for hardware-based multi-layer neural networks. The conductance response of NAND flash cells is measured and it is shown that the unidirectional conductance response is suitable for implementing multi-layer neural networks using NAND flash memory cells as synaptic devices. Using an online-learning, we obtained higher learning accuracy with NAND synaptic devices compared to that with a memristor-based synapse regardless of weight update methods. Using an adaptive weight update method based on a unidirectional conductance response, we obtained a 94.19% learning accuracy with NAND synaptic devices. This accuracy is comparable to 94.69% obtained by synapses based on the ideal perfect linear device. Therefore, NAND flash memory which is mature technology and has great advantage in cell density can be a promising synaptic device for implementing high-density multi-layer neural networks. INDEX TERMS Neuromorphic, NAND flash memory, deep neural networks (DNNs), synaptic device, deep learning, multi-layer neural networks, hardware-based neural network.