László Horváth started swimming in 1957 in the III. District TTVE. After finding swimming monotonous Horváth switched to the modern pentathlon in the Újpesti Dózsa from 1964. He won the individual national championship title in 1972, as well as in 1974-75 and 1977. He was elected Hungarian modern pentathlete of the year in 1977 and 1979. In 1973, as a member of the Hungarian team, he won the world championship bronze, which was followed by another third place in 1977. In the same year he won a modern pentathlon competition in London with 5,695 points, which was the highest individual score achieved in the sport up to that point. In 1979 the team won the silver medal at the World Championship in Budapest, followed by the 1980 Moskva Olympics, where the team again won the silver medal behind the Soviet team.
After the Olympics, Horváth became a coach at Újpesti Dózsa, and two years later he was also the national captain of the junior national team. Between 1989 and 1991 he was the head coach of the senior team. In 1992 he founded the triathlon department of Újpesti Dózsa, changing sports after 20 years.