In 1980 Alsup purchased the inventory of WASP Racing and started his own team called Alsup Racing, Alsup driving the #41 Polaroid Time Zero Penske PC7-Cosworth DFX. He started the season by finishing sixth in the season opening Dastun Twin 200 at Ontario Motor Speedway. He failed to qualify for the Indianapolis 500, rebounded to finish third at the Red Roof Inns 150 at Mid-Ohio Sports Car Course, and finished the season seventh in points, earning him the CART Most Improved Driver Award.