Advanced paternal age has been associated with a variety of rare conditions and diseases of great public health impact. An increased number of de novo point mutations in sperm with increasing age have been suggested as a mechanism, which would likely also affect fetal viability. We examined the association between paternal age and stillbirth rate in a large nationwide cohort. We identified all pregnancies in Denmark from 1994 to 2010 carried to a gestational age of at least 22 completed weeks (n = 944,031) as registered in national registers and linked to individual register data about the parents. The hazard ratio of stillbirth according to paternal age was estimated, adjusted for maternal age in 1-year categories, year of outcome, and additionally parental educational levels. The relative rate of stillbirth (n = 4946) according to paternal age was found to be J-shaped with the highest hazard ratio for fathers aged more than 40 years when paternal age was modelled using restricted cubic splines. When modelled categorically, the adjusted hazard ratios of stillbirth were as follows: <25, 1.16 (95% confidence interval, CI 1.01–1.34); 25–29, 1.03 (95% CI 0.95–1.11); 35–39, 1.16 (95% CI 1.07–1.26); 40–44, 1.41 (95% CI 1.26–1.59); 45–49, 1.20 (95% CI 0.97–1.49); 50+, 1.58 (95% CI 1.18–2.11), compared with fathers aged 30–34 years. These estimates attenuated slightly when further adjusted for parental education. Our study showed that paternal age was associated with the relative rate of stillbirth in a J-shaped manner with the highest hazard ratios among fathers aged more than 40 years.