Tibetan sheep are mainly distributed in the Qinghai鈥揟ibet Plateau. Its meat is not only essential for the local people but also preferred by the non-inhabitant of this plateau also. To investigate the salient development features and molecular mechanism of the meat difference of LT muscle caused by different growth stages in Tibetan sheep, the carcass performance, meat quality, and comparative transcriptome analysis were performed for investigating the potential molecular mechanism of the meat quality difference of the LT muscle caused by four growth stages [4-months old (4 months), 1.5-years old (1.5 years), 3.5-years old (3.5 years), and 6-years old (6 years)] in the Tibetan sheep. The shear force increased with the increase of age (p < 0.05) while the intramuscular fat (IMF) was the highest at 1.5 y. The AMPK signaling pathway was significantly enriched in the four comparative groups. The weighted gene co-expression network analysis (WGCNA) results showed that the hub genes P4HA2, FBXL4, and PPARA were identified to regulate the meat quality. In summary, 1.5 years was found to be the most suitable slaughter age of the Tibetan sheep which ensured better meat tenderness and higher IMF content. Moreover, the genes LIPE, LEP, ADIPOQ, SCD, and FASN may regulate the transformation of the muscle fiber types through the AMPK signaling pathway, further affecting the meat quality.