The 1960 Atlantic hurricane season was the least active season since 1952. The season officially began on June 15, and lasted until November 15. These dates conventionally delimit the period of each year when most tropical cyclones form in the Atlantic basin. The first system, an unnamed storm, developed in the Bay of Campeche on June 22. It brought severe local flooding to southeastern Texas and was considered the worst disaster in some towns since a Hurricane in 1945. The unnamed storm moved across the United States for almost a week before dissipating on June 29. In July, Hurricane Abby resulted in minor damage in the Leeward Islands, before impacting a few Central American counties — the remnants of the storm would go on to form Hurricane Celeste in the East Pacific. Later that month, Tropical Storm Brenda caused flooding across much of the East Coast of the United States. The next storm, Hurricane Cleo, caused no known impact, despite its close proximity to land.

The Atlantic hurricane season is the period in a year, from June 1 through November 30, when tropical or subtropical cyclones are most likely to form in the North Atlantic Ocean. These dates, adopted by convention, encompass the period in each year when most tropical cyclogenesis occurs in the basin. Even so, subtropical or tropical cyclogenesis is possible at any time of the year, and often does occur.