González has competed in a total of six Summer Paralympics, first competing in the 1992 Games in Barcelona where he won bronze in the 200m and 400m C8 sprints and silver in the C5-C8 100m relay. In Atlanta in 1996 he again competed in the relay and 200m but his only medal was a second bronze in the 400m. This would prove to be his last medal as he failed to medal in the 400m or either relay in the 2000 Summer Paralympics, at the 2004 Summer Paralympics he competed in the 400m, 800m and 4 × 400 m relay and at the 2008 Summer Paralympics he competed in the 800m.