Angustinaripterus was discovered at Dashanpu near Zigong in the Szechuan province of China. It is known from a single skull. Angustinaripterus was named in 1983 by He Xinlu. The type species is Angustinaripterus longicephalus. The genus name is derived from Latin angustus, "narrow" and naris, "nostril", combined with Latinized Greek pteron, "wing". The specific name is derived from Latin longus, "long", and Greek kephale, "head".