Artemisia arborescens L. is a medicinal and aromatic plant used in traditional medicine for its therapeutic properties to treat lung diseases, gastrointestinal disorders, diabetes and inflammations. The leaves of A. arborescens L. were harvested in Amizour, Cap Bouak and Sahel (Bejaia, Algeria) and their essential oils were analyzed by Gas Chromatography/Flame Ionization Detector and Gas Chromatography/Mass Spectrometry. The main constituents were β-thujone in the essential oil of Cap Bouak (59.8%), camphor in the volatile oil of Sahel (58.7%) and chamazulene in that of Amizour (31.4%). The radical scavenging activity of these essential oils was evaluated against DPPH and ABTS radicals by calculation of IC50. The best activity against DPPH and ABTS radicals were that of Sahel essential oil with IC50 DPPH = 133.0 µg/mL and IC50 ABTS = 211.6 µg/mL. The Spearman test revealed no significant correlations between IC50 DPPH and the chemical composition of the essential oil from A. arborescens L., while correlations with IC50 ABTS indicated that hydrocarbon monoterpenes, oxygenated monoterpenes and hydrocarbon sesquiterpenes promote activity against ABTS radical. These results can give prospects of using essential oils from A. arborescens L. as a natural adjunct in medicine formulations to treat diseases caused by oxidative stress.