A new and distinct cultivar of hibiscus plant named ‘DUP-ASP’, characterized by glossy, dark green leaves, upright growth, and a very large flower characterized by a medium-sized, slightly glossy medium red eye which extends approximately one quarter of the petal length, the eye rays extending through a light pinkish purple zone extending to one third the petal length, grading into a greenish brown zone, which grades into a brownish orange zone at the petal edge.