Understanding the genetic architecture of beef cattle growth cannot be limited simply to the genome-wide association study (GWAS) for body weight at any specific ages, but should be extended to a more general purpose by considering the whole growth trajectory over time using a growth curve approach. For such an approach, the parameters that are used to describe growth curves were treated as phenotypes under a GWAS model. Data from 1,255 Brahman cattle that were weighed at birth, 6, 12, 15, 18, and 24 months of age were analyzed. Parameter estimates, such as mature weight (A) and maturity rate (K) from nonlinear models are utilized as substitutes for the original body weights for the GWAS analysis. We chose the best nonlinear model to describe the weight-age data, and the estimated parameters were used as phenotypes in a multi-trait GWAS. Our aims were to identify and characterize associated SNP markers to indicate SNP-derived candidate genes and annotate their function as related to growth processes in beef cattle. The Brody model presented the best goodness of fit, and the heritability values for the parameter estimates for mature weight (A) and maturity rate (K) were 0.23 and 0.32, respectively, proving that these traits can be a feasible alternative when the objective is to change the shape of growth curves within genetic improvement programs. The genetic correlation between A and K was -0.84, indicating that animals with lower mature body weights reached that weight at younger ages. One hundred and sixty seven (167) and two hundred and sixty two (262) significant SNPs were associated with A and K, respectively. The annotated genes closest to the most significant SNPs for A had direct biological functions related to muscle development (RAB28), myogenic induction (BTG1), fetal growth (IL2), and body weights (APEX2); K genes were functionally associated with body weight, body height, average daily gain (TMEM18), and skeletal muscle development (SMN1). Candidate genes emerging from this GWAS may inform the search for causative mutations that could underpin genomic breeding for improved growth rates.