A neural network operation apparatus and method implementing quantization is disclosed. The neural network operation method may include receiving a weight of a neural network, a candidate set of quantization points, and a bitwidth for representing the weight, extracting a subset of quantization points from the candidate set of quantization points based on the bitwidth, calculating a quantization loss based on the weight of the neural network and the subset of quantization points, and generating a target subset of quantization points based on the quantization loss.