| Date | Location | Result | |
| Jan 2, 1978 | Dallas, Texas | Notre Dame 38, Texas 10 | Box score |
| Nov 26, 1977 | College Staion, TX | Texas 57, Texas A&M 28 | Box score |
| Nov 19, 1977 | Austin, Texas | Texas 29, Baylor 7 | Box score |
| Nov 12, 1977 | Austin, Texas | Texas 44, TCU 14 | Box score |
| Nov 5, 1977 | Houston, Texas | Texas 35, Houston 21 | Box score |
| Oct 29, 1977 | Austin, Texas | Texas 26, Texas Tech 0 | Box score |
| Oct 22, 1977 | Dallas, Texas | Texas 30, SMU 14 | Box score |
| Oct 15, 1977 | Fayetteville, AR | Texas 13, Arkansas 9 | Box score |
| Oct 8, 1977 | Dallas, Texas | Texas 13, Oklahoma 6 | Box score |
| Oct 1, 1977 | Austin, Texas | Texas 72, Rice 15 | Box score |
| Sep 17, 1977 | Austin, Texas | Texas 68, Virginia 0 | Box score |
| Sep 10, 1977 | Austin, Texas | Texas 44, Boston College 0 | Box score |