Tan sheep are greatly preferred by consumers in China because of their nutritional value and unique flavor. However, the meat quality of Tan sheep has decreased due to the change in feeding systems from grazing to indoor. Studies investigating the mechanisms for the decrease in meat quality are limited. A total of 28 Tan sheep were randomly allocated to two treatments, receiving a concentrated diet, or pasture. Flavor precursors and volatile compounds were analyzed with foodomics. E-nose and E-tongue analyses suggested that the aroma and taste profiles differed between the feeding systems. The grazing lambs had higher levels of linoleic acid and n-3 polyunsaturated fatty acids (p p < 0.01). These results reveal key changes in flavor precursors and flavor profiles affected by the feeding system, which may provide an initial view of the reason for consumer preference for the grazing Tan sheep.