Discriminating the matched named entity pairs or identifying the entities' canonical forms are critical in text mining tasks. More precise named entity normalization in text mining will benefit other subsequent text analytic applications. We built the named entity normalization model with a novel edge weight updating neural network. We, next, verify our model's performance on NCBI disease, BC5CDR disease, and BC5CDR chemical databases, which are widely used named entity normalization datasets in the bioinformatics field. We also tested our model with our own financial named entity normalization dataset to validate the efficacy for more general applications. Using the constructed dataset, we differentiate named entity pairs. Our model achieved the highest named entity normalization performances in terms of various evaluation metrics. Our proposed model when tested on four different datasets achieved state-of-the-art results.