CRISPR gene drives have potential for widespread and cost-efficient pest control, but are highly controversial. We examined a potential gene drive targeting spermatogenesis to control the invasive common wasp (Vespula vulgaris) in New Zealand. Vespula wasps are haplodiploid. Their life cycle makes gene drive production challenging, as nests are initiated by single fertilized queens in spring followed by several cohorts of sterile female workers and the production of reproductives in autumn. We show that different spermatogenesis genes have different levels of variation between introduced and native ranges, enabling a potential ‘precision drive’ that could target the reduced genetic diversity and genotypes within the invaded range. In vitro testing showed guide-RNA target specificity and efficacy that was dependent on the gene target within Vespula, but no cross-reactivity in other Hymenoptera. Mathematical modelling incorporating the genetic and life history traits of Vespula wasps identified characteristics for a male sterility drive to achieve population control. There was a trade-off between drive infiltration and impact: a drive causing complete male sterility would not spread, while partial sterility could be effective in limiting population size if the homing rate is high. Our results indicate that gene drives may offer viable suppression for wasps and other haplodiploid pests.