Kwon emerged as a frontrunner and a medal contender at the 2001 Summer Universiade in Beijing, China, where he took home the gold in the 81-kg class against Azerbaijan's Mehman Azizov.

[2][3] Two years later, Kwon defeated Spain's Óscar Fernández for an unprecedented second straight gold in his respective division.

[4] Kwon qualified for the South Korean squad in the men's half-middleweight class (81 kg) at the 2004 Summer Olympics in Athens, by placing third and receiving a berth from the Asian Championships in Almaty, Kazakhstan.

He thwarted France's Cédric Claverie and Cuba's Gabriel Arteaga in the prelims by a waza-ari and a yuko score, before being sanctioned with a penalty and falling short to Greek judoka and eventual Olympic champion Ilias Iliadis in a sudden-death quarterfinal match.

[5] In the repechage round, Kwon ran off from his temporary falter with an effortless victory over Australia's Morgan Endicott-Davies, but fell short in a tremendous ippon to Brazilian judoka Flávio Canto within twenty-seven seconds, ending him in the seventh spot.