The effects of different feeding regimes on antioxidant activity, meat quality, fatty acid composition, lipid oxidation, and volatile matter production in the longissimus thoracis (LT) of Sunit sheep at 0, 24, 48, 72, and 96 h postmortem were investigated. The results showed that the activity of antioxidant enzymes, tenderness, water retention, and percentage of unsaturated fatty acids were significantly higher in the pasture-fed sheep (PF) than in the concentrate-fed sheep (CF) (p < 0.05). During postmortem aging, antioxidant activity, water retention, and the proportion of unsaturated fatty acids decreased in the PF and CF (p < 0.05), while malondialdehyde (MDA) content, the proportion of saturated fatty acids, and the content of flavor substances resulting from fat oxidation increased. After 24 h of LT muscle aging, the pH and shear force of the meat started to increase and the color stabilized. The differences between shear force values and lipid volatile flavor substance content of sheep meat under different feeding regimes disappeared with increasing aging time. PF had better oxidative stability and fatty acid composition. Postmortem aging changed the oxidative stability of sheep meat, thus affecting meat quality and fatty acid composition and consequently meat flavor composition, while aging also eliminated to some extent the differences caused by feeding regimes.