Increasing evidence indicates that sexual coercion is widespread. While some coercive strategies are conspicuous, such as forced copulation or sexual harassment, less is known about the ecology and evolution of intimidation, where repeated male aggression promotes future rather than immediate mating success with targeted females. Although known in humans, intimidation was recently reported in chimpanzees (Pan troglodytes) and chacma baboons (Papio ursinus), where males are regularly violent against females. Here, we investigate the nature of male coercive strategies in wild mandrills (Mandrillus sphinx), a primate living in large polygynandrous groups where severe male aggression towards females is rare and females can form coalitions against males. Yet, we found support for all three predictions of the sexual coercion hypothesis, namely that male aggression (1) specifically targets sexually receptive females, (2) inflicts costs to these females, and (3) increases male mating success in the long-term. These results hold true when considering only non-physical threats, or only severe aggression. Finally, we show that high-ranking females are most targeted by males, probably because of their higher reproductive performances, while high-ranking males are most coercive. These results indicate that sexual intimidation is widespread in sexually dimorphic and group-living mammals, and that males and females vary in their propensities to use, and to be exposed to sexual coercion, respectively.