Fruit seeds belonging to the pomegranate cultivar “Granata” were subjected to extraction and oily component analysis, with the aim of obtaining information about their composition. The presence of conjugated isomers of linolenic acid (CLNA isomers) in the oily phase extracted from the seeds gives a high added value to this part of the fruit, which is too often considered and treated as waste. The separated seeds were subjected to a classic Soxhlet extraction with n-hexane or extraction with supercritical CO2, assisted by ethanol. The resulting oils were evaluated by 1H and 13C-NMR and AP-MALDI-MS techniques. Differences in the triacylglycerols composition, with particular regard to punicic acid and other CLNA content, were studied in depth. Results showed the prevalence of punicic acid in the triacylglycerol mixture up to the 75%, with clear preponderance in the extract by supercritical fluids. Consequently, other CLNA isomers are, altogether, two-fold less represented in the supercritical extract than in the Soxhlet one. The two oily residues were subjected to solid phase extraction (SPE) and to HPLC-DAD analysis for the polyphenolic isolation and characterization. In addition to HPLC analysis, which showed different content and composition, DPPH analysis to evaluate the antiradical potential showed that the extract obtained with supercritical CO2 was much more active.