The adulteration and traceability of olive oils are serious problems in the olive oil industry. In this work, a method based on laser-induced breakdown spectroscopy (LIBS) and neural networks (NNs) has been developed and applied to the identification, quality control, traceability, and adulteration detection of extra virgin olive oils. Instant identification of the samples is achieved using a spectral library, which was obtained by analysis of representative samples using a single laser pulse and treatment by NNs. The samples used in this study belong to four countries. The study also included different regions of each country. The results obtained allow the identification of the oils tested with a certainty of more than 95%. Single-shot measurements were enough for clear identification of the samples. The method can be developed for automatic real-time, fast, reliable, and robust measurements, and the system can be packed into portable form for non-specialist users.