Background: There is great potential for the genetic improvement of oil palm yield. Traditional progeny tests allow accurate selection but limit the number of individuals evaluated. Genomic selection (GS) could overcome this constraint. We estimated the accuracy of GS prediction of seven oil yield components using A × B hybrid progeny tests with almost 500 crosses for training and 200 crosses for independent validation. Genotyping-by-sequencing (GBS) yielded +5000 single nucleotide polymorphisms (SNPs) on the parents of the crosses. The genomic best linear unbiased prediction method gave genomic predictions using the SNPs of the training and validation sets and the phenotypes of the training crosses. The practical impact was illustrated by quantifying the additional bunch production of the crosses selected in the validation experiment if genomic preselection had been applied in the parental populations before progeny tests. Results: We found that prediction accuracies for cross values plateaued at 500 to 2000 SNPs, with high (0.73) or low (0.28) values depending on traits. Similar results were obtained when parental breeding values were predicted. GS was able to capture genetic differences within parental families, requiring at least 2000 SNPs with less than 5% missing data, imputed using pedigrees. Genomic preselection could have increased the selected hybrids bunch production by more than 10%. Conclusions: Finally, preselection for yield components using GBS is the first possible application of GS in oil palm. This will increase selection intensity, thus improving the performance of commercial hybrids. Further research is required to increase the benefits from GS, which should revolutionize oil palm breeding.