The Jessup Competition was the brainchild of Professor Richard R. Baxter at Harvard Law School, who worked with Professor Stephen M. Schwebel (later President of the International Court of Justice) to create a courtroom simulation experience grounded in international law.

Originally named the "International Law Moot," the Jessup Competition held its first round at Harvard University on 8 May 1960. The round, comprised only of Harvard Law students, involved a team of two American law students, Thomas J. Farer and William Zabel, and a team of two foreign LL.M. students, Ivan L. Head of Canada and Bernard H. Clark of New Zealand. The first Jessup problem was titled, "Cuban Agrarian Reform Case." Since then, the Jessup Competition has been held annually, and student participation has increased dramatically.

Shortly after the first Jessup Competition, the idea of creating an organization to serve the needs of students interested in international law arose. In 1962, students from a number of campuses founded the Association of Student International Law Societies. The Association evolved over the years, and in 1987, reconstituted itself as the International Law Students Association (ILSA). In May 1994, ILSA incorporated as a non-profit organization in the District of Columbia in response to its rapid expansion and development.