Predicting genetic variances of biparental populations has been a long-standing goal for plant breeders. The ability to discriminate among crosses with similarly predicted high means but different levels of genetic variance (VG) should improve the effectiveness of breeding. We developed a procedure that uses established progeny simulation and genomic predictionstrategies to predict the population mean (µ) and VG, the mean of the desired 10% of the progeny (superior progeny mean [µ sp]), and correlated responses of multiple traits for biparental populations. The proposed procedure, PopVar, is herein demonstrated using a training population (TP) composed of 383 breeding lines that have been genotyped and phenotyped for yield and deoxynivalenol (DON). Marker effects estimated from the TP were used to calculate genotypic estimated breeding values (GEBVs) of 200 simulated recombinant inbred lines (RILs) per cross. Values of µ, VG, and µ sp were then calculated directly from the RIL GEBVs. We found that µ explaned 82 and 88% of variation in µ sp for yield and DON, respectively, and adding VG to the regression model increased those respective R2 values to 99.5 and 99.6%. The results of correlated response revealed that although yield and DON are unfavorably correlated, the correlation was near zero or slightly negative in some simulated crosses, indicating the potential to increase yield while decreasing DON. This work extends the current benefits of genomic selection to include the ability to design crosses that maximize genetic variance with more favorable correlations among traits. PopVar is available as an R package that researchers and breeders are encouraged to use for empirical evaluation of the methodology.