Gruss grew up in the town of Alsfeld in the German state of Hesse. After gaining his university-entrance qualification ("Abitur"), he embarked on a degree in biology at Darmstadt University of Technology in 1968, graduating from the Institute of Microbiology in 1973. From 1974 to 1977, Peter Gruss worked on his Ph.D. on the subject of a tumor virus at the Institute for Virus Research at the German Cancer Research Center (DKFZ) in Heidelberg. He then spent a year as an assistant at the German Cancer Research Center. In 1978 he went to the US as a post doc in receipt of a fellowship grant to continue studying tumor viruses at the Cancer Institute of the National Institutes of Health (NIH) in Bethesda/Maryland.