Oil palm breeding relies on reciprocal recurrent selection between two heterotic groups complementary for bunch number and average bunch weight. Given the long generation interval and the limited selection intensity imposed by the progeny tests currently used in the program, genomic selection (GS) is a very promising solution for this species. However, GS also accelerates the annual increase in inbreeding in oil palm parental populations. This can generate inbreeding depression, which can be detrimental for seed production, and cause the loss of favourable alleles, which can reduce the long-term genetic progress. Here, we investigated the effect of three approaches of inbreeding management on parental inbreeding and genetic progress in hybrids. We simulated two widely used parental populations, La Mé and Deli, and four generations of selection. Inbreeding was measured in La Mé and genetic progress on hybrids bunch production. Inbreeding management in La Mé was made by: (i) mate selection, which uses the simulated annealing optimization algorithm, (ii) limiting deterministically the number of full-sibs selected and (iii) prohibiting selfings. The results showed that all methods slowed down the increase in parental inbreeding. Mate selection was also able to simultaneously increase the genetic progress. Stronger slowing-down in inbreeding were achieved with deterministic methods, in particular by selecting at best one individual per full-sib family and prohibiting selfings. However, this was associated with a decreased genetic progress. Finally, mate selection will allow oil palm breeders to control the rate of increase in inbreeding in the parental populations while maximizing the genetic gain.