The growth rate of sheep determines their productivity; the faster the growth rate, the higher the productivity. Sheep growth is usually measured by body weight, which is an important indicator of overall growth, and body size, which reflects body shape and structure. Therefore, in sheep production, the selection and improvement of growth traits is one of the important means to improve production efficiency. In this study, 857 males of Hu sheep were selected to record growth traits, including body weight, height, length, and chest, and cannon circumference at 80, 100, 120, 140, 160 and 180 days of age, as well as live weight before slaughter and carcass weight. Correlation analyses conducted between these growth traits at different stages were significantly correlated with both live weight before slaughter and carcass weight. And the strongest correlation was observed for body weight, while body height showed the weakest correlation. The myosin heavy chain 3 (MYH3) gene in the MYH gene family was selected as the target gene, and a synonymous mutation (MYH3 g.33834192A>G) in the exon 12 region of MYH3 was identified by polymerase chain reaction (PCR) and Sanger sequencing. Further association analysis using competitive allele-specific PCR (KASPar) technique showed that the MYH3 g.33834192A>G locus was significantly (P < 0.05) associated with growth traits (including body weight from 80 to 160 days of age, body height at 80 and 100 days of age, body length at 100 and 140 days of age, chest circumference at 80, 100, 160, and 180 days of age, cannon circumference at 80–140 days of age and carcass weight). Among them, the dominant genotype was GG. Meanwhile, the tissue expression results indicated that the highest level of MYH3 gene expression was found in muscle tissues. Therefore, this locus can be used as a candidate molecular genetic marker for improving growth traits in Hu sheep.