Thompson was born in Jacksonville, Florida, and moved to Washington, D.C., to study art at Howard University. There, Thompson studied with the pioneering African American art historian James Porter. Thompson received her Bachelor’s degree from Howard in 1957. She also studied at the prestigious Skowhegan School of Painting and Sculpture as well as the Brooklyn Museum Art School. From 1958 to 1961, she studied at the Hochschule für bildende Künste in Hamburg, Germany, where she learned different printmaking techniques.

After a brief return to the U.S., Thompson struggled to find acceptance as an artist in New York. Due to rising racial tensions, she returned to Germany in 1963. Thompson’s work became increasingly abstract, and she began constructing her “wood pictures”—assemblages of found wood fashioned into geometric compositions. Thompson lived, worked, and taught art and art history in Düren, Germany, until 1975, when she returned to Florida and was artist-in-residence of the City of Tampa. From 1977 to 1978, she was the artist-in-residence at Howard University. Thompson divided her time between various studios in Washington, D.C., and Paris, France, between 1979 and 1985. She settled in Atlanta in 1985, where she became an artist-in-residence at Spelman College, later taught at the Atlanta College of Art, and worked as associate editor at Art Papers magazine.