Parker was born in Beresford, South Dakota. He received his BA in 1946 from the University of Iowa and, two years later, his MFA. His first solo exhibition was held at the Walker Arts Center, Minneapolis in 1950, and he exhibited widely thereafter, including solo exhibitions at the Dayton Art Institute in 1965 and the San Francisco Museum of Art in 1967.
His work from the 1960s, described by the artist as "simple paintings", consist of areas of roughly-formed oblongs or ovals suspended in the picture plane, with paint applied with rags. In the mid-1960s though, Parker developed works with more form and color, and felt liberated to experiment with elaborate shapes and even more varied colors. A trend which he continued into the 1970s.
In addition to painting, Parker was also a printmaker and, begining in the late-1960s, he produced at least a dozen different lithographs.