Bancroft opened as a school in 1912. The building was named after American historian and Nebraska pioneer George Bancroft.
The school served the Omaha community as a junior high school from 1964 – 1986. In 1976, the year busing started, students who lived in the Castelar, Jackson, Kellom, Lincoln, Mason, and Train attendance areas attended Bancroft for 7th, 8th, and 9th grades. Rosewater and Vinton students just attended Bancroft in 9th grade. Bancroft was rebuilt in 1988 at the cost of $6.2 million. The school was reopened as an elementary school with students from pre-kindergarten through 6th grade.