The 1978 Thunderbird Classic was a women's singles tennis tournament played on outdoor hard courts at the Arizona Biltmore Hotel in Phoenix, Arizona in the United States.

The event was part of the AA[a] category of the 1978 Colgate Series.

It was the eighth edition of the tournament and was held from October 2 through October 8, 1978.

[2] First-seeded Martina Navratilova won the singles title and earned $14,000 first-prize money.

[2][1] Martina Navratilova defeated Tracy Austin 6–4, 6–2 Tracy Austin / Betty Stöve defeated Martina Navratilova / Anne Smith 6–4, 6–7, 6–2