Nothing is known of him until 1526, when he married the daughter of Ludwig Nöggi, a master carpenter who sat in the city council, and Asper himself was a citizen of some standing, being elected to the Great Council in 1545.
He is thought to have studied with Hans Leu the Younger, in Zürich, and appears to have received early influence in portrait painting from the works of Hans Holbein the Younger.
His first artworks date from 1531, with possibly the most well-known portrait of Swiss reformator Huldrych Zwingli, painted with oil on parchment.
In the same year Asper painted the interiors of some of Zürich's government buildings, being at the time the official painter to the city.
Asper is also believed to have provided the illustrations for Conrad Gesner's Historia Animalium.