Recurrent selection is an important breeding method for population improvement and selecting elite inbreds or fixed lines from the improved germplasm. Recently, a computer simulation tool called QuMARS has been developed, which allows the simulation and optimization of various recurrent selection strategies. Our major objective in this study was to use the QuMARS tool to compare phenotypic recurrent, marker-assisted recurrent, and genomic selections (abbreviated respectively as PS, MARS and GS) for both short- and long- term breeding procedures. For MARS, two marker selection models were considered, i.e., stepwise (Rstep) and forward regressions (Forward). For GS, three prediction models were considered, i.e., genomic best linear unbiased predictors (GBLUP), ridge regression (Ridge), and regression by Moore-Penrose general inverse (InverseMP). To generate genotypes and phenotypes for a given individual during simulation, one additive and two epistasis genetic models were considered with three levels of heritability. Results demonstrated that selection responses from GBLUP-based GS and MARS (Forward) were consistently greater than those from PS under the additive model, particularly in early selection cycles. In contrast, selection response from PS was consistently superior over MARS and GS under epistatic models. For the two epistasis models, total genetic variance and the additive variance component were increased in some cases after selection. Through simulation, we concluded that GS and PS were effective recurrent selection methods for improved breeding of targeted traits controlled by additive and epistatic quantitative trait loci (QTL). QuMARS provides an opportunity for breeders to compare, optimize and integrate new technology into their conventional breeding programs.