Brown-marbled grouper, Epinephelus fuscoguttatus, is not only an important commercial fish species, but also an important crossbreeding parent in grouper industry. Improvement of growth traits of this species contributes to the development of grouper breeding. Currently, the development of molecular marker associated with growth of brown-marbled grouper is rare. Thus, we performed the first genome-wide association study (GWAS) for five growth traits in 172 brown-marbled groupers with 43,688 SNPs detected by ddRAD-seq. We identified a total of 5 significant and 18 suggestive QTLs located in multiple chromosomes associated with growth traits. In the 20 kb window of the significant SNPs and suggestive SNPs, 5 and 14 potential candidate genes affecting growth were detected, respectively. Five potential candidate genes near the significantly associated SNPs were selected for expression analysis. Among of which, bmp2k, wasf1, and acyp2 involved in bone development, maintenance of mitochondrion structure, and metabolism were differentially expressed. Interestingly, the SNP 23:29601315 located in the intron of bmp2k was significantly associated with body weight, body length, body height, and body thickness and suggestively associated with total length. We verified the locus using another new group including 123 individuals. The results showed that individuals with CC genotype have better growth traits comparing other individuals. Our findings not only contribute to understanding the molecular mechanism of growth regulation, but also promote the advance of marker-assisted selection in brown-marbled grouper.