 On November 10, 1972, he took on Chango Carmona for the WBC Lightweight Title and won via a Corner retirement in the 13th round.González defended the title two times before losing the belt to Guts Ishimatsu on April 11, 1974, via KO in the 8 round.Later in the year he rematched Ishimatsu, but lost via TKO and retired from boxing.