Complex traits with multiple phenotypic values changing over time are called longitudinal traits. In traditional genome-wide association studies (GWAS) for longitudinal traits, a combined/averaged estimated breeding value (EBV) or deregressed proof (DRP) instead of multiple phenotypic measurements per se for each individual was frequently treated as response variable in statistical model. This can result in power losses or even inflate false positive rates (FPRs) in the detection due to failure of exploring time-dependent relationship among measurements. Aiming at overcoming such limitation, we developed two random regression-based models for functional GWAS on longitudinal traits, which could directly use original time-dependent records as response variable and fit the time-varied Quantitative Trait Nucleotide (QTN) effect. Simulation studies showed that our methods could control the FPRs and increase statistical powers in detecting QTN in comparison with traditional methods where EBVs, DRPs or estimated residuals were considered as response variables. Besides, our proposed models also achieved reliable powers in gene detection when implementing into two real datasets, a Chinese Holstein Cattle data and the Genetic Analysis Workshop 18 data. Our study herein offers an optimal way to enhance the power of gene detection and further understand genetic control of developmental processes for complex longitudinal traits.