The obscure puffer (Takifugu obscurus) is a popular cultured species and accounts for around 50% of the total pufferfish production in China. A hybrid puffer was generated by crossing a female obscure puffer with a male tiger puffer (T. rubripes). Its growth model has not been developed and the genetic basis underlying its growth superiority has not yet been fully investigated. In this study, the growth model and morphological traits of the hybrid puffer were explored. The results indicated that the hybrid puffer exhibited a significant growth advantage compared to the obscure puffer. There were also significant differences in their morphological traits. We conducted genotyping-by-sequencing (GBS) on hybrid and obscure puffer groups, identifying 215,288 high-quality single nucleotide polymorphisms (SNPs) on 22 chromosomes. Subsequently, a total of 13 growth-related selection regions were identified via a combination of selection signatures and a genome-wide association study (GWAS); these regions were mainly located on chromosomes 10 and 22. Ultimately, the screened regions contained 13 growth-related genes, including itgav, ighv3-43, ighm, atp6v1b2, pld1, xmrk, inhba, dsp, dsg2, and dsc2, which regulate growth through a variety of pathways. Taken together, the growth models and candidate genes used in this study will aid our understanding of production characteristics and the genetic basis of growth rates. The hybrid will also be of great significance for the genome-assisted breeding of pufferfish in the future.