Sheep growth performance, mainly skeletal muscle growth, provides direct economic benefits to the animal husbandry industry. However, the underlying genetic mechanisms of different breeds remain unclear. We found that the cross-sectional area (CSA) of skeletal muscle in Dorper (D) and binary cross-breeding (HD) was higher than that in Hu sheep (H) from 3 months to 12 months after birth. The transcriptomic analysis of 42 quadriceps femoris samples showed that a total of 5053 differential expression genes (DEGs) were identified. The differences in the global gene expression patterns, the dynamic transcriptome of skeletal muscle development, and the transcriptome of the transformation of fast and slow muscles were explored using weighted correlation network analysis (WGCNA) and allele-specific expression analysis. Moreover, the gene expression patterns of HD were more similar to D rather than H from 3 months to 12 months, which might be the reason for the difference in muscle growth in the three breeds. Additionally, several genes (GNB2L1,RPL15,DVL1,FBXO31, etc.) were identified as candidates related to skeletal muscle growth. These results should serve as an important resource revealing the molecular basis of muscle growth and development in sheep.