Dubravko Šimenc's father Zlatko was a water polo player who won the silver medal at the 1964 Summer Olympics playing for Yugoslavia, and also a professor at the Faculty of Kinesiology. Šimenc's mother was a volleyball player. As a boy, Šimenc played many different sports. He started to play water polo in 1975.
Šimenc's first major medal was silver in the 1985 European Championships with Yugoslavia. The following year, his club Mladost won the World Champion title in Madrid.