Mutations generate sequence diversity and provide a substrate for selection. The rate of de novo mutations is therefore of major importance to evolution. Here we conduct a study of genome-wide mutation rates by sequencing the entire genomes of 78 Icelandic parent-offspring trios at high coverage. We show that in our samples, with an average father’s age of 29.7, the average de novo mutation rate is 1.20 × 10−8 per nucleotide per generation. Most notably, the diversity in mutation rate of single nucleotide polymorphisms is dominated by the age of the father at conception of the child. The effect is an increase of about two mutations per year. An exponential model estimates paternal mutations doubling every 16.5 years. After accounting for random Poisson variation, father’s age is estimated to explain nearly all of the remaining variation in the de novo mutation counts. These observations shed light on the importance of the father’s age on the risk of diseases such as schizophrenia and autism.