| Date | Location | Result | |
| Dec 23, 1978 | El Paso, Texas | Texas 42, Maryland 0 | Box score |
| Dec 1, 1978 | Austin, Texas | Texas 22, Texas A&M 7 | Box score |
| Nov 25, 1978 | Waco, Texas | Baylor 38, Texas 14 | Box score |
| Nov 18, 1978 | Fort Worth, Texas | Texas 41, TCU 0 | Box score |
| Nov 11, 1978 | Austin, Texas | Houston 10, Texas 7 | Box score |
| Oct 28, 1978 | Austin, Texas | Texas 22, SMU 3 | Box score |
| Oct 21, 1978 | Austin, Texas | Texas 28, Arkansas 21 | Box score |
| Oct 14, 1978 | Austin, Texas | Texas 26, North Texas State 16 | Box score |
| Oct 7, 1978 | Dallas, Texas | Oklahoma 31, Texas 10 | Box score |
| Sep 30, 1978 | Lubbock, Texas | Texas 24, Texas Tech 7 | Box score |
| Sep 23, 1978 | Austin, Texas | Texas 17, Wyoming 3 | Box score |
| Sep 16, 1978 | Houston, Texas | Texas 34, Rice 0 | Box score |