Growth is a complex trait with moderate to high heritability in livestock and must be described by the longitudinal data measured over multiple time points. Therefore, the used phenotype in genome-wide association studies (GWAS) of growth traits could be either the measures at the preselected time point or the fitted parameters of whole growth trajectory. A promising alternative approach was recently proposed that combined the fitting of growth curves and estimation of single-nucleotide polymorphism (SNP) effects into single-step nonlinear mixed model (NMM). In this study, we collected the body weights at 35, 42, 49, 56, 63, 70, and 84 days of age for 401 animals in a crossbred population of meat rabbits and compared five fitting models of growth curves (Logistic, Gompertz, Brody, Von Bertalanffy, and Richards). The logistic model was preferably selected and subjected to GWAS using the approach of single-step NMM, which was based on 87,704 genome-wide SNPs. A total of 45 significant SNPs distributed on five chromosomes were found to simultaneously affect the two growth parameters of mature weight (A) and maturity rate (K). However, no SNP was found to be independently associated with either A or K. Seven positional genes, including KCNIP4, GBA3, PPARGC1A, LDB2, SHISA3, GNA13, and FGF10, were suggested to be candidates affecting growth performances in meat rabbits. To the best of our knowledge, this is the first report of GWAS based on single-step NMM for longitudinal traits in rabbits, which also revealed the genetic architecture of growth traits that are helpful in implementing genome selection.