Griffin was selected in the 1st round (4th overall) in the 1966 January Regular Baseball Draft by the Houston Astros out of Grant High School, in Los Angeles, California.

[citation needed] He pitched seven innings while striking out eight and walking five and allowing two runs on three hits, but the Padres prevailed 2–0.

[1] In that season, he would go 11–10 with a 3.54 ERA in 31 games, pitching 188.1 innings while striking out 200 batters and walking 93, with the latter two being highs for Griffin.

[citation needed] He went 5–6 that year, having a 3.91 ERA in 59 games (3 starts) as he garnered two saves in 94.1 innings, striking out 82 with 46 walks.

[citation needed] The following year, he went 5–1 with a 2.76 ERA in 42 games (four starts) in 107.2 innings as he struck out 79 with 49 walks, although he led the league in hit batsmen with eight.

[citation needed] In 1981, he went 8–8 with a 3.76 ERA in 22 games (all starts) in 129.1 innings while striking out 83 and walking 57 and leading the league in hit batsmen with seven.

[citation needed] He pitched four innings while allowing three earned runs with one strikeout and six walks as the losing pitcher in a 4–2 Astros win.