Genomic selection is promising for plant breeding, particularly for perennial crops. Multivariate analysis, which considers several traits jointly, takes advantage of the genetic correlations to increase accuracy. The aim of this study was to empirically evaluate the potential of a univariate and multivariate genomic mixed model (G-BLUP) compared to the traditional univariate pedigree-based BLUP (T-BLUP) when analyzing progeny tests of oil palm, the world's major oil crop. The dataset comprised 478 crosses between two heterotic groups, A and B, with 140 and 131 parents, respectively, genotyped with 313 simple sequence repeat markers. The traits were bunch number and average bunch weight. We found that G-BLUP with a genomic matrix based on a similarity index gave a higher likelihood than T-BLUP. In addition, multivariate G-BLUP improved the accuracy of additive effects (breeding values or general combining abilities, GCAs), in particular for the less heritable trait, and of dominance effects (specific combining abilities, SCAs). The average increase in accuracy was 22.5 % for GCAs and 18.7 % for SCAs. Using 160 markers in group A and 90 in group B was enough to reach maximum GCA prediction accuracy. The contrasted history of the parental groups likely explained the higher benefit of G-BLUP over T-BLUP for group A than for group B. Finally, G-BLUP should be used instead of T-BLUP to analyze oil palm progeny tests, with a multivariate approach for correlated traits. G-BLUP will allow breeders to consider SCAs in addition to GCAs when selecting between the progeny-tested parents.