László Szabados tried several sports (athletics, tennis, rowing, hockey) in his hometown at a young age, but ended up as a competitive swimmer. He continued his high school and then university studies in Budapest and obtained a doctorate title in law from the Pázmány Péter University. In 1929, as a swimmer of MUE he reached the second place in 100-meter freestyle in the national high school championship. Next year he moved to UTE. With his new club Szabados he won the Hungarian championship six times in relay.
Between 1931 and 1934 he was a member of the national swimming team seven times and during this period he became European champion in the 4x200m relay in 1931 and won Olympic bronze medal the following year in the same discipline. In 1933 and 1935 he was world college champion.
After his active sport career, he worked as a legal advisor.