Predation has direct effects on prey population dynamics through mortality, and it can induce indirect effects through fear. The indirect effects of predation have been documented experimentally, but few studies have quantified them in nature so that their role in prey population dynamics remains controversial. Given the expanding or reintroduced populations of large predators in many areas, the quantification of indirect effects of predation is crucial. We sought to evaluate the direct and indirect fitness effects of intense cougar (Puma concolor) predation using 48 years of data on marked bighorn sheep (Ovis canadensis) on Ram Mountain, Alberta, Canada. We compared years of intense cougar predation with years with no or occasional cougar predation. We first quantified the effects of predation on neonatal, weaning, and overwinter lamb survival, three metrics potentially affected by direct and indirect effects. We then investigated the possible indirect effects of intense cougar predation on lamb production, female summer mass gain, and lamb mass at weaning. We found strong effects of cougar predation on lamb survival, lamb production, and seasonal mass gain of lambs and adult females. In years with high predation, neonatal, weaning, and overwinter lamb survival declined by 18.4%, 19.7% and 20.8%, respectively. Indirect effects included a 14.2% decline in lamb production. Female summer mass gain decreased by 15.6% and lamb mass at weaning declined by 8.0% in years of intense cougar predation. Our findings bring key insights on the impacts of predation on prey fitness by reporting moderate to large effects on recruitment and illustrate the importance of indirect effects of predation on population dynamics.