Nakayama was born in Fujieda on September 23, 1967. After graduating from University of Tsukuba, he joined Japan Soccer League club Yamaha Motors (later Júbilo Iwata) in 1990. In 1992, Japan Soccer League was folded and the club joined new league, Japan Football League. In 1993, the club won the 2nd place and was promoted to J1 League from 1994. The club won the J1 League champions in 1997, 1999 and 2002. In 1998, he scored 36 goals in 27 matches and became a top scorer. He was also selected MVP award. He also became a top scorer in 2000. This was golden era in the club history and he was one of the central player in golden era. From later 2000s, his opportunity to play decreased. In 2010, he moved to J2 League club Consadole Sapporo at the age of 43. Although the club was promoted to J1 in 2012, he could not play many matches in 3 seasons and retired end of 2012 season. In 2015, he came back as player at Japan Football League club Azul Claro Numazu. The club was promoted to J3 League in 2017. He retired end of 2020 season again without playing in the match at the club.
On July 31, 1990, Nakayama debuted for the Japan national team against North Korea. In 1992, he was selected the Japan for 1992 Asian Cup which held in Japan. He scored 2 goals in the tournament and Japan team won the champions. In 1993, he played at 1994 World Cup qualification in Doha. However Japan failed to qualify for the 1994 World Cup. It was known as the "Agony of Doha" (ドーハの悲劇) in Japan. In November 1997, he scored 2 goals for Japan during 1998 World Cup qualification final round and playoff, leading the Japan to their first ever World Cup. At the 1998 World Cup, Nakayama scored the only goal of the tournament and the first goal for Japan in the history of the World Cup against Jamaica on June 26. He also played at 2001 Confederations Cup and 2002 World Cup which held in Japan. He played 53 games and scored 21 goals for Japan until 2003.