The 1978 Texas Tech Red Raiders football team represented Texas Tech University as a member of the Southwest Conference (SWC) during the 1978 NCAA Division I-A football season. In their first season under head coach Rex Dockery, the Red Raiders compiled a 7âÂÂ4 record (5âÂÂ3 against SWC opponents), were outscored by a combined total of 268 to 246, and finished in fourth place in the conference. The team played its home games at Clifford B. and Audrey Jones Stadium in Lubbock, Texas.