Welding is one of the most complex industrial processes because it is challenging to model, control, and inspect. In particular, the quality inspection process is critical because it is a complex and time-consuming activity. This research aims to propose a system of online inspection of the quality of the welded items with gas metal arc welding (GMAW) technology through the use of neural networks to speed up the inspection process. In particular, following experimental tests, the deviations of the welding parameters—such as current, voltage, and welding speed—from the Welding Procedure Specification was used to train a fully connected deep neural network, once labels have been obtained for each weld seam of a multi-pass welding procedure through non-destructive testing, which made it possible to find a correspondence between welding defects (e.g., porosity, lack of penetrations, etc.) and process parameters. The final results have shown an accuracy greater than 93% in defects classification and an inference time of less than 150 ms, which allow us to use this method for real-time purposes. Furthermore in this work networks were trained to reach a smaller false positive rate for the classification task on test data, to reduce the presence of faulty parts among non-defective parts.