Phenotypic backcrossing for a quantitative trait is generally ineffective. An alternative approach is to use genomewide predictions to identify which plants should be crossed to the recurrent parent to form each successive backcross generation. My objective was to assess the amount of genetic gain achieved from the use of genomewide predictions during backcrossing for a quantitative trait. Simulation experiments were conducted with an adapted line as the recurrent parent and an exotic line as the donor parent. Compared with the expected allele frequencies in the absence of selection, genomewide selection during backcrossing increased the frequency of favorable alleles from the donor parent and slightly decreased the frequency of favorable alleles from the recurrent parent. The selection response (R), expressed as a standardized deviation from the performance of the recurrent parent, ranged from -1.44 to 1.76. Unless the number of QTL was large and the donor parent was very poor, the R values were positive as long as an F2 training population was used and all of the markers were included in the genomewide predictions. Lines derived from the BC6 to BC8 generation typically had <4 favorable alleles introgressed from the donor parent. Notably, the improved lines carried different subsets of favorable alleles from the donor parent. The approach described herein is most appropriate when a breeder aims to largely retain the genetic background and characteristics of the recurrent parent, with only incremental improvements that enhance the recurrent parent for quantitative traits.