Advanced paternal age (APA) and intelligence quotient (IQ) are both associated with the risk of schizophrenia spectrum disorder (SSD) in young adult offspring. We hypothesized that the offspring SSD risk gradient associated with paternal age is mediated by offspring IQ. We investigated joint and separate associations of paternal age and offspring IQ with the risk of SSD. We used IQ routinely measured at conscription in Danish males (n=138,966) from cohorts born in 1955-84 and in 1976-1993 and followed them from a year after the conscription through 2010. We used Cox regression to estimate the incidence rate ratio (IRR) of SSD. During the follow-up, 528 men developed SSD (incidence rate [IR] 5.2 and 8.6 per 10,000 person-years in the first and second cohorts, respectively). APA was associated with higher risk of SSD (IRR, 1.32; 95% CI, 1.10-1.60 per a ten-year increase in paternal age). A higher IQ was associated with lower SSD risk (IRR, 0.68; 95% confidence interval [CI], 0.63-0.74 per one SD increase). The IR of SSD was higher among persons who were draft-exempt for health reasons (<20% of the men). Overall, there was little evidence of lower premorbid IQ in APA-related SSD (individuals who developed SSD and were also offspring of older fathers). Our results do not support the notion that risk gradient for offspring SSD associated with paternal age is mediated by offspring IQ.